Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: 2/(x-2)=3/(x+2)
=>3x-6=2x+4
=>x=10
b: (x-2)(x+5)=0
=>x-2=0 hoặc x+5=0
=>x=2 hoặc x=-5
c: 2(x+2)-x=4
=>2x+4-x=4
=>x=0
\(a,\dfrac{2}{x-2}=\dfrac{3}{x+2}\)
\(\Leftrightarrow\dfrac{2}{x-2}-\dfrac{3}{x+2}=0\)
\(\Leftrightarrow\dfrac{2\left(x+2\right)-3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow2x+4-3x+6=0\)
\(\Leftrightarrow-x+10=0\)
\(\Leftrightarrow-x=-10\)
\(\Leftrightarrow x=10\)
\(b,\left(x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
\(c,2\left(x+2\right)-x=4\)
\(\Leftrightarrow2x+4-x-4=0\)
\(\Leftrightarrow x=0\)
Ta có:
(2 - 3x)(x + 8) = (3x - 2)(3 - 5x)
⇔ (2 - 3x)(x + 8) - (3x - 2)(3 - 5x) = 0
⇔ (2 - 3x)(x + 8) + (2 - 3x)(3 - 5x) = 0
⇔ (2 - 3x)(x + 8 + 3 - 5x) = 0
⇔ (2 - 3x)(11 - 4x) = 0
⇔ 2 - 3x = 0 hay 11 - 4x = 0
⇔ 2 = 3x hay 11 = 4x
⇔ x = \(\dfrac{2}{3}\) hay x = \(\dfrac{11}{4}\)
Vậy tập nghiệm của pt S = \(\left\{\dfrac{2}{3};\dfrac{11}{4}\right\}\)
<=> (2-3x ) (x+8) + (2-3x ) (3-5x)=0
<=> (2-3x ) ( x+8 + 3-5x ) =0
<=> (2-3x ) ( 11 - 4x ) = 0
=> 2-3x =0 hoặc 11-4x =0
3x = 2 4x =11
x = 2/3 x = 11/4
ĐKXĐ:\(x\ne-2\)
\(\dfrac{1}{x+2}-1=\dfrac{5x+7}{x+2}\\ \Leftrightarrow\dfrac{1}{x+2}-\dfrac{5x+7}{x+2}=1\\ \Leftrightarrow\dfrac{1-5x-7}{x+2}=1\\ \Leftrightarrow-5x-6=x+2\\ \Leftrightarrow x+2+5x+6=0\\ \Leftrightarrow6x+8=0\\ \Leftrightarrow x=-\dfrac{4}{3}\left(tm\right)\)
thank
\(ĐK:x\ne\dfrac{1}{2};x\ne1;x\ne\dfrac{3}{2};x\ne2;x\ne\dfrac{5}{2}\\ PT\Leftrightarrow\dfrac{1}{\left(2x-1\right)\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(3x-2\right)}+\dfrac{1}{\left(3x-2\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(5x-2\right)}=\dfrac{4}{21}\\ \Leftrightarrow2\left[\dfrac{\dfrac{1}{2}}{\left(x-\dfrac{1}{2}\right)\left(x-1\right)}+\dfrac{\dfrac{1}{2}}{\left(x-1\right)\left(x-\dfrac{3}{2}\right)}+\dfrac{\dfrac{1}{2}}{\left(x-\dfrac{3}{2}\right)\left(x-2\right)}+\dfrac{\dfrac{1}{2}}{\left(x-2\right)\left(x-\dfrac{5}{2}\right)}\right]=\dfrac{4}{21}\)
\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-\dfrac{1}{2}}+\dfrac{1}{x-\dfrac{3}{2}}-\dfrac{1}{x-1}+\dfrac{1}{x-2}-\dfrac{1}{x-\dfrac{3}{2}}+\dfrac{1}{x-\dfrac{5}{2}}-\dfrac{1}{x-2}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-\dfrac{5}{2}}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{x-\dfrac{5}{2}-x+1}{\left(x-1\right)\left(x-\dfrac{5}{2}\right)}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{-\dfrac{3}{2}}{x^2-\dfrac{7}{2}x+\dfrac{5}{2}}=\dfrac{2}{21}\\ \Leftrightarrow x^2-\dfrac{7}{2}x+\dfrac{5}{2}=-\dfrac{63}{4}\\ \Leftrightarrow4x^2-14x+10=-63\\ \Leftrightarrow4x^2-14x+73=0\\ \Leftrightarrow x\in\varnothing\)
\(5x-\frac{1}{3x}+2=5x-\frac{7}{3}x-1\)
\(\Rightarrow5x-\frac{1}{3x}+2-5x+\frac{7}{3x}+1=0\)
\(\Rightarrow\frac{6}{3x}+3=0\)
\(\Rightarrow\frac{2}{x}+3=0\)
\(\Rightarrow\frac{2}{x}=-3\)
\(\Rightarrow x=\frac{-2}{3}\)
\(\frac{5x-1}{3x+2}=\frac{5x-7}{3x-1}\) (1)
ĐKXĐ :
\(\hept{\begin{cases}3x+2\ne0\\3x-1\ne0\end{cases}}\Rightarrow\hept{\begin{cases}3x\ne-2\\3x\ne1\end{cases}\Rightarrow\hept{\begin{cases}x\ne\frac{-2}{3}\\x\ne\frac{1}{3}\end{cases}}}\)
Từ (1) ta có :
\(\Rightarrow\left(5x-1\right).\left(3x-1\right)=\left(3x+2\right).\left(5x-7\right)\)
\(\Leftrightarrow15x^2-8x+1=15x^2-11x-14\)
\(\Leftrightarrow15x^2-15x^2-8x+11x=-14-1\)
\(\Leftrightarrow3x=-15\)
\(\Leftrightarrow x=-15:3\)
\(\Leftrightarrow x=-5.\)( t/m ĐKXĐ )
Vậy phương trình có tập nghiệm là \(S=\left\{-5\right\}\).
\(\Leftrightarrow\frac{6x^2+3}{24}-\frac{10x-4}{24}=\frac{6x^2-6}{24}-\frac{4x-12}{24}\)
\(\Leftrightarrow\frac{6x^2+3-10x+4}{24}=\frac{6x^2-6-4x+12}{24}\)
\(\Leftrightarrow6x^2-10x+7=6x^2-4x+6\)
\(\Leftrightarrow-6x+1=0\)
\(\Rightarrow-6x=-1\)
\(\Leftrightarrow x=\frac{1}{6}\)
Vậy ...
Bài 2:
Vì x = 4 là nghiệm của phương trình \(4x+3m=-x+1\)
nên thay x = 4 vào phương trình, ta được:
\(4.4+3m=-4+1\)
\(\Leftrightarrow16+3m=-3\)
\(\Leftrightarrow3m=-3-16\)
\(\Leftrightarrow3m=-19\Leftrightarrow m=\dfrac{-19}{3}\)
Vậy m = \(\dfrac{-19}{3}\) là giá trị cần tìm
⇒4y+6=6+5
⇒4y=5x
⇒y=\(\dfrac{5x}{4}\)=1,25x
⇒x=\(\dfrac{4y}{5}\)=0.8y