bài 1: thực hiện phép tính
a, x+1/2x+6 + 2x
b, 3/2x+6 - x-6/2x^2+6x
c, x/x-2y + x/x+2y + 4xy/4y^2-x^2
d, 1/3x-2 - 1/3x+2 - 3x-6/4-9x^2
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21 tháng 5 2017
a)\(\dfrac{x+1}{2x+6}\)+\(\dfrac{2x+3}{x^2+3x}\)
\(2x+6=2\left(x+3\right)\)
\(x^2+3x=x\left(x+3\right)\)
MC:\(2x\left(x+3\right)\)
\(\dfrac{x^2+x}{2x\left(x+3\right)}\)+\(\dfrac{2\times\left(2x+3\right)}{2x\left(x+3\right)}\)=0
\(\Leftrightarrow x^2+x+4x+6\)=0
\(\Leftrightarrow x^2+5x+6\)=0
\(\Leftrightarrow x^2+2x+3x+6\)=0
\(\Leftrightarrow\left(x^2+2x\right)+\left(3x+6\right)\)=0
\(\Leftrightarrow x\left(x+2\right)+3\left(x+2\right)\)=0
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow x+2=0\) hoặc \(x+3=0\)
\(\Leftrightarrow x+2=0\Rightarrow x=-2\)
\(\Leftrightarrow x+3=0\Rightarrow x=-3\)
S={-2;-3}
8 tháng 9 2021
\(a,-2xy^2\left(x^3y-2x^2y^2+5xy^3\right)\\ =-2x^4y^3+4x^3y^4-10x^2y^5\\ b,\left(-2x\right)\left(x^3-3x^2-x+1\right)\\ =-2x^4+6x^3+2x^2-2x\\ c,\left(-10x^3+\dfrac{2}{5}y-\dfrac{1}{3}z\right)\left(-\dfrac{1}{2}zy\right)\\ =5x^3yz-\dfrac{1}{5}y^2z+\dfrac{1}{6}yz^2\\ d,3x^2\left(2x^3-x+5\right)=6x^5-3x^3+15x^2\\ e,\left(4xy+3y-5x\right)x^2y=4x^3y^2+3x^2y^2-5x^3y\\ f,\left(3x^2y-6xy+9x\right)\left(-\dfrac{4}{3}xy\right)\\ =-4x^3y^2+8x^2y^2-12x^2y\)
2 tháng 12 2023
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
\(a.\dfrac{x+1}{2x+6}+2x=\dfrac{x+1+4x^2+12x}{2x+6}=\dfrac{4x^2+13x+1}{2x+6}\) ( x # -3)
\(b.\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\) ( x # - 3)
Các câu còn lại tương tự .
\(a,\dfrac{x+1}{2x+6}+2x\)
\(=\dfrac{x+1}{2x+6}+\dfrac{2x\left(2x+6\right)}{2x+6}\)
\(=\dfrac{x+1+4x^2+12x}{2x+6}\)
\(=\dfrac{4x^2+13x+1}{2x+6}\)
\(b,\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
\(=\dfrac{3x}{2x^2+6x}-\dfrac{x-6}{2x^2-6x}\)
\(=\dfrac{2x-6}{2x^2+6x}=\dfrac{2\left(x-3\right)}{2x\left(x+3\right)}=\dfrac{x-3}{x^2+3x}\)
\(c,\dfrac{x}{x-2y}+\dfrac{x}{x+2y}+\dfrac{4xy}{4y^2-x^2}\)
\(=\dfrac{x\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\dfrac{x\left(x-2y\right)}{\left(x+2y\right)\left(x-2y\right)}-\dfrac{4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{2x^2-4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{2x\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{2x}{x+2y}\)
\(d,\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{4-9x^2}\)
\(=\dfrac{3x+2}{\left(3x+2\right)\left(3x-2\right)}-\dfrac{3x-2}{\left(3x+2\right)\left(3x-2\right)}+\dfrac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\dfrac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{3x-2}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{1}{3x+2}\)