Rút gọn các phân thức sau:a) \(\dfrac{5x}{10}\)b)\(\dfrac{4xy}{2y}\) (y≠0)c)\(\dfrac{5x-5y}{3x-3y}\) (x≠y)d) \(\dfrac{x^2-y^2}{x y}\)(chưa có điều kiện xác định)e) \(\dfrac{x^3-x^2 x-1}{x^2-1}\)(chưa...

2

MH

Minh Hiếu

15 tháng 9 2023

a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)

b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)

c) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5}{3}\left(x\ne y\right)\)

d) \(\dfrac{x^2-y^2}{x+y}=x-y\left(đk:x\ne-y\right)\)

e) \(\dfrac{x^3-x^2+x-1}{x^2-1}=\dfrac{x^2+1}{x+1}\left(đk:x\ne\pm1\right)\)

f) \(\dfrac{x^2+4x+4}{2x+4}=\dfrac{x+2}{2}\left(đk:x\ne-2\right)\)

NL

Nguyễn Lê Phước Thịnh

15 tháng 9 2023

loading...

bài 11.rút gọn biểu thức:\(a,\dfrac{9x^2}{11y^2}:\dfrac{3x}{2y}:\dfrac{6x}{11y}\) \(b,\dfrac{3x+15y}{x^3-y^3}:\dfrac{x+5y}{x-y}\) \(c,\dfrac{x^2-1}{x^2-4x+4}:\dfrac{x+1}{2-x}\) \(d,\dfrac{5x+10}{x+2}:\dfrac{5y}{x}\) \(e,\dfrac{2x}{3x-3y}:\dfrac{x^2}{x-y}\) \(f,\dfrac{5x-3}{4x^2y}-\dfrac{x-3}{4x^2y}\) \(g,\dfrac{3x+10}{x+3}-\dfrac{x+4}{x+3}\) \(h,\dfrac{4}{x-1}+\dfrac{2}{1-x}+\dfrac{x}{x-1}\) ...

TL

thùy linh

16 tháng 12 2022

1, Rút gọn các phân thức sau : a, \(\dfrac{5x}{10}\) b, \(\dfrac{4xy}{2y}\) ( y # 0) c, \(\dfrac{21x^2y^3}{6xy}\) ( xy # 0) d, \(\dfrac{2x+2y}{4}\) e, \(\dfrac{5x-5y}{3x-3y}\) ( x # y) f, \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}\) ( x # y) 2, Rút gọn các phân thức sau : a, \(\dfrac{x^2-16}{4x-x^2}\) ( x # 0, x # 4) b, \(\dfrac{x^2+4x+3}{2x+6}\) ( x # -3) c, \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}\) ( y + ( x+y) # 0) d,...

1

NL

Nguyễn Lê Phước Thịnh

16 tháng 12 2022

f: \(=\dfrac{5x-3-x+3}{4x^2y}=\dfrac{4x}{4x^2y}=\dfrac{1}{xy}\)

g: \(=\dfrac{3x+10-x-4}{x+3}=\dfrac{2x+6}{x+3}=2\)

h: \(=\dfrac{4-2+x}{x-1}=\dfrac{x+2}{x-1}\)

n: \(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{x\left(x+3\right)}=\dfrac{2}{x}\)

p: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)

k: \(=\dfrac{x-2x-4+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{-6}{x^2-4}\)

m: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)

Đúng(2)

AV

Ánh Vũ Ngọc

7 tháng 11 2017

1

HL

Hà Linh

7 tháng 11 2017

1)

a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)

b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)

c) \(\dfrac{21x^2y^3}{6xy}=\dfrac{7xy^2}{2}\left(xy\ne0\right)\)

d) \(\dfrac{2x+2y}{4}=\dfrac{2\left(x+y\right)}{4}=\dfrac{x+y}{2}\)

e) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5\left(x-y\right)}{3\left(x-y\right)}=\dfrac{5}{3}\left(x\ne y\right)\)

f) \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}=-5x\dfrac{x-y}{y-x}=-5x\dfrac{x-y}{-\left(x-y\right)}\)

\(=-5x.\left(-1\right)=5x\left(x\ne y\right)\)

2)

a) Nhớ ghi ĐK vào nhá, lười quá :V\(\dfrac{x^2-16}{4x-x^2}=-\dfrac{\left(x-4\right)\left(x+4\right)}{x^2-4x}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(x-4\right)}=\dfrac{x+4}{x}\)

b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

c) \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+3\right)^3}{y\left(x+y\right)^2}\) ( câu này có gì đó sai sai )

d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)

e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)

\(=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)

TN

Thơ Nụ =))

30 tháng 1

Rút gọn:

\(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\)

\(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)

\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)

\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)

1

NL

Nguyễn Lê Phước Thịnh

30 tháng 1

\(\dfrac{2a\cdot x^2-4ax+2a}{5b-5bx^2}\)

\(=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\)

\(=\dfrac{-2a\left(x-1\right)^2}{5b\left(x-1\right)\left(x+1\right)}=\dfrac{-2a\left(x-1\right)}{5b\left(x+1\right)}\)

\(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)

\(=\dfrac{4x\cdot x-4x\cdot y}{5x^2\cdot x-5x^2\cdot y}\)

\(=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)

\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)

\(=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}\)

=x+y-z

\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)

\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)

\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3+y^3\right)\left(x^3-y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)

Đúng(2)

CI

Cíu iem

6 tháng 10 2021

Rút gọn các phân thức sau:
a)  \(\dfrac{6x^2y^2}{8xy^{ }5}\)
b) \(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
c)  \(\dfrac{2x^2+2x }{x+1}\)
d)  \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)
e)  \(\dfrac{36\left(x-2\right)^3}{32-16x}\)

1

LL

Lấp La Lấp Lánh

6 tháng 10 2021

a) \(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)

b) \(=\dfrac{2y}{3\left(x+y\right)^2}=\dfrac{2y}{3x^2+6xy+3y^2}\)

c) \(=\dfrac{2x\left(x+1\right)}{x+1}=2x\)

d) \(=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)

e) \(=\dfrac{36\left(x-2\right)^3}{-16\left(x-2\right)}=-9\left(x-2\right)^2=-9x^2+36x-36\)

A = \(\dfrac{5xy^2-3z}{3xy}+\dfrac{4x^2y+3z}{3xy}\)B = \(\dfrac{3y+5}{y-1}+\dfrac{-y^2-4y}{1-y}+\dfrac{y^2+y+7}{y-1}\)C = \(\dfrac{6x}{x^2-9}+\dfrac{5x}{x-3}+\dfrac{x}{x+3}\)D = \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)E...

CI

Cíu iem

18 tháng 10 2021

1

NL

Nguyễn Lê Phước Thịnh

18 tháng 10 2021

b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)

\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)

\(=\dfrac{2y^2+8y+12}{y-1}\)

BÀI 6 :rút gọn phân thức\(\dfrac{x^3+3x^3+3x+1}{x^2+x}\)b)\(\dfrac{x^3-3x^2+3x-1}{2x-2}\)c)\(\dfrac{x^2+4x+4}{2x+4}\)d)\(\dfrac{(x-1)(-x-2)}{x+2}\)e)\(\dfrac{x^2-y^2}{x+y}\)f)\(\dfrac{3x^2+4xy^2}{6x+8y}\)g)\(\dfrac{-3x^2-6x}{4-x^2}\)BÀI 7 :quy đồng mẫu thức các phân thức\(\dfrac{2}{5x^3y^2}và \dfrac{3}{4xy}\)b)\(\dfrac{x}{x^2-2xy+y^2} và \dfrac{x}{x^2-xy}\)c)\(\dfrac{1}{x+2};\dfrac{2}{2x+4}và \dfrac{3}{3x+6}\)d)\(\dfrac{1}{x+3};\dfrac{2}{2x-6}và...

KL

Khánh Linh Đỗ

26 tháng 10 2023

Làm tính trừ phân thức...

1

NL

Nguyễn Lê Phước Thịnh

26 tháng 10 2023

6:

a: ĐKXĐ: x<>0

\(\dfrac{x^3+3x^2+3x+1}{x^2+x}\)

\(=\dfrac{\left(x+1\right)^3}{x\left(x+1\right)}=\dfrac{\left(x+1\right)^2}{x}\)

b: ĐKXĐ: x<>1

\(\dfrac{x^3-3x^2+3x-1}{2x-2}\)

\(=\dfrac{\left(x-1\right)^3}{2\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{2}\)

c: ĐKXĐ: x<>-2

\(\dfrac{x^2+4x+4}{2x+4}\)

\(=\dfrac{\left(x+2\right)^2}{2\left(x+2\right)}\)

\(=\dfrac{x+2}{2}\)

d: ĐKXĐ: x<>-2

\(\dfrac{\left(x-1\right)\left(-x-2\right)}{x+2}\)

\(=\dfrac{\left(-x+1\right)\left(x+2\right)}{x+2}=-x+1\)

e: ĐKXĐ: x<>-y

\(\dfrac{x^2-y^2}{x+y}=\dfrac{\left(x-y\right)\left(x+y\right)}{x+y}=x-y\)

g: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

\(\dfrac{-3x^2-6x}{4-x^2}=\dfrac{3x^2+6x}{x^2-4}\)

\(=\dfrac{3x\left(x+2\right)}{\left(x+2\right)\cdot\left(x-2\right)}=\dfrac{3x}{x-2}\)

7:

a: \(\dfrac{2}{5x^3y^2}=\dfrac{2\cdot4}{20x^3y^2}=\dfrac{8}{20x^3y^2}\)

\(\dfrac{3}{4xy}=\dfrac{3\cdot5\cdot x^2y}{20x^3y^2}=\dfrac{15x^2y}{20x^3y^2}\)

b: \(\dfrac{x}{x^2-2xy+y^2}=\dfrac{x}{\left(x-y\right)^2}\)

\(\dfrac{x}{x^2-xy}=\dfrac{x}{x\left(x-y\right)}=\dfrac{1}{x-y}=\dfrac{\left(x-y\right)}{\left(x-y\right)^2}\)

c: \(\dfrac{1}{x+2}=\dfrac{6}{6\left(x+2\right)}\)

\(\dfrac{2}{2x+4}=\dfrac{2}{2\left(x+2\right)}=\dfrac{1}{x+2}=\dfrac{6}{6\left(x+2\right)}\)

\(\dfrac{3}{3x+6}=\dfrac{3}{3\left(x+2\right)}=\dfrac{6}{6\left(x+2\right)}\)

d:

\(\dfrac{2}{2x-6}=\dfrac{2}{2\left(x-3\right)}=\dfrac{1}{x-3};\dfrac{3}{3x-9}=\dfrac{3}{3\left(x-3\right)}=\dfrac{1}{x-3}\)

\(\dfrac{2}{2x-6}=\dfrac{1}{x-3}=\dfrac{x+3}{\left(x-3\right)\left(x+3\right)}\)

\(\dfrac{3}{3x-9}=\dfrac{1}{x-3}=\dfrac{x+3}{\left(x-3\right)\left(x+3\right)}\)

\(\dfrac{1}{x+3}=\dfrac{x-3}{\left(x+3\right)\left(x-3\right)}\)

Đúng(2)

SG

Sách Giáo Khoa

28 tháng 4 2017

1

NT

Nguyen Thuy Hoa

28 tháng 6 2017

Phép trừ các phân thức đại số

1.tìm điều kiện xác định của các bt saua,5x^2y/x+4 b,3x-2y/2x-1 c,5x^2/x(y-3) d,4x^3y/x^2-4y^2 e,2x+1/(5-x)(y+2)2.rút gọn các phân thứca,-12x^3y^2/-20x^2y^2 b,x^2+xy-x-y/x^2-xy-x+y c,7x^2-7xy/y^2-x^2 d,7x^2+14x+7/3x^2+3x e,3y-2-3xy+2x/1-3x-x^3+3x^2 f,x^10-x^8+x^6-x^4+x^2+1/x^4-1 ...

N

nghia

21 tháng 1

1

NL

Nguyễn Lê Phước Thịnh

21 tháng 1

Bài 1:

a: ĐKXĐ: \(x+4\ne0\)

=>\(x\ne-4\)

b: ĐKXĐ: \(2x-1\ne0\)

=>\(2x\ne1\)

=>\(x\ne\dfrac{1}{2}\)

c: ĐKXĐ: \(x\left(y-3\right)\ne0\)

=>\(\left\{{}\begin{matrix}x\ne0\\y-3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\y\ne3\end{matrix}\right.\)

d: ĐKXĐ: \(x^2-4y^2\ne0\)

=>\(\left(x-2y\right)\left(x+2y\right)\ne0\)

=>\(x\ne\pm2y\)

e: ĐKXĐ: \(\left(5-x\right)\left(y+2\right)\ne0\)

=>\(\left\{{}\begin{matrix}x\ne5\\y\ne-2\end{matrix}\right.\)

Bài 2:

a: \(\dfrac{-12x^3y^2}{-20x^2y^2}=\dfrac{12x^3y^2}{20x^2y^2}=\dfrac{12x^3y^2:4x^2y^2}{20x^2y^2:4x^2y^2}=\dfrac{3x}{5}\)

b: \(\dfrac{x^2+xy-x-y}{x^2-xy-x+y}\)

\(=\dfrac{\left(x^2+xy\right)-\left(x+y\right)}{\left(x^2-xy\right)-\left(x-y\right)}\)

\(=\dfrac{x\left(x+y\right)-\left(x+y\right)}{x\left(x-y\right)-\left(x-y\right)}=\dfrac{\left(x+y\right)\left(x-1\right)}{\left(x-y\right)\left(x-1\right)}\)

\(=\dfrac{x+y}{x-y}\)

c: \(\dfrac{7x^2-7xy}{y^2-x^2}\)

\(=\dfrac{7x\left(x-y\right)}{\left(y-x\right)\left(y+x\right)}\)

\(=\dfrac{-7x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{-7x}{x+y}\)
d: \(\dfrac{7x^2+14x+7}{3x^2+3x}\)

\(=\dfrac{7\left(x^2+2x+1\right)}{3x\left(x+1\right)}\)

\(=\dfrac{7\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)}{3x}\)

e: \(\dfrac{3y-2-3xy+2x}{1-3x-x^3+3x^2}\)

\(=\dfrac{3y-2-x\left(3y-2\right)}{1-3x+3x^2-x^3}\)

\(=\dfrac{\left(3y-2\right)\left(1-x\right)}{\left(1-x\right)^3}=\dfrac{3y-2}{\left(1-x\right)^2}\)

g: \(\dfrac{x^2+7x+12}{x^2+5x+6}\)

\(=\dfrac{\left(x+3\right)\left(x+4\right)}{\left(x+3\right)\left(x+2\right)}\)

\(=\dfrac{x+4}{x+2}\)

TY

Thiên Yến Thần

25 tháng 8 2021

1. Tìm hàm số xác định của các hàm số sau.

a) \(y=\dfrac{x}{x^2-3x+2}\)

b)\(y=\dfrac{x-1}{2x^2-5x+2}\)

c)\(y=\dfrac{x-1}{x^3+1}\)

d) \(y=\dfrac{1}{x^4+2x^2-3}\)

e) \(y=\sqrt{x+3-2\sqrt{x+2}}\)

#Toán lớp 10

1

B

bepro_vn

25 tháng 8 2021

a)x khác 1;2 b)x khác 2;1/2 c)x khác -1 d)x khác 1 e x>/=-2