Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
=\(\left(\frac{x}{\left(x-5\right).\left(x+5\right)}-\frac{\left(x-5\right)}{x.\left(x+5\right)}\right).\frac{x^2+5x}{2x-5}\)
=\(\left(\frac{x^2}{x.\left(x-5\right).\left(x+5\right)}-\frac{\left(x-5\right)^2}{x.\left(x-5\right).\left(x+5\right)}\right).\frac{x\left(x+5\right)}{2x-5}\)
=\(\frac{x^2-\left(x-5\right)^2}{x.\left(x-5\right).\left(x+5\right)}.\frac{x.\left(x+5\right)}{2x-5}\)
=\(\frac{\left(x-x+5\right).\left(x+x-5\right)}{x.\left(x-5\right)\left(x+5\right)}.\frac{x.\left(x+5\right)}{2x+5}\)
=\(\frac{5.\left(2x-5\right).x\left(x+5\right)}{x.\left(x-5\right).\left(x+5\right).\left(2x-5\right)}\)
=\(\frac{5}{x+5}\)
a, (2x+5)mũ 2=(x+2) mũ 2
=.> (2x+5) mũ 2-(x+2) mũ 2=0
=> (2x+5+x+2)x(2x+5-x-2)=0
=>(3x+7)x(x+3)=0
=>3x+7=0 hoặc x+3=0
3x+7=0=>x=-7/3
x+3=0 =>x=-3
vậy x=-7/3 hoặc x=-3
hok tot
1.
\(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)
\(MC:12\)
Quy đồng :
\(\Rightarrow\frac{3.\left(2x+3\right)}{12}-\left(\frac{2.\left(5x+3\right)}{12}\right)=\frac{3x-4}{12}\)
\(\frac{6x+9}{12}-\left(\frac{10x+6}{12}\right)=\frac{3x-4}{12}\)
\(\Leftrightarrow6x+9-\left(10x+6\right)=3x-4\)
\(\Leftrightarrow6x+9-3x=-4-9+16\)
\(\Leftrightarrow-7x=3\)
\(\Leftrightarrow x=\frac{-3}{7}\)
2.\(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)
\(MC:20\)
Quy đồng :
\(\frac{15.\left(2x+1\right)}{20}-\frac{20}{20}=\frac{2.\left(15x-1\right)}{20}\)
\(\Leftrightarrow15\left(2x+1\right)-20=2\left(15x-1\right)\)
\(\Leftrightarrow30x+15-20=15x-2\)
\(\Leftrightarrow15x=3\)
\(\Leftrightarrow x=\frac{3}{15}=\frac{1}{5}\)
\(A=\left(\frac{x}{x^2-25}-\frac{x-5}{x^2+5x}\right):\frac{2x-5}{x^2+5x}+\frac{x+3}{5-x}\)
\(=\left[\frac{x}{\left(x-5\right)\left(x+5\right)}-\frac{x-5}{x\left(x+5\right)}\right]:\frac{2x-5}{x\left(x+5\right)}+\frac{x+3}{5-x}\)
\(=\left[\frac{x^2}{x\left(x-5\right)\left(x+5\right)}-\frac{\left(x-5\right)^2}{x\left(x+5\right)\left(x-5\right)}\right]:\frac{2x-5}{x\left(x+5\right)}+\frac{x+3}{5-x}\)
\(=\left(\frac{x^2-\left(x-5\right)^2}{x\left(x-5\right)\left(x+5\right)}\right).\frac{x\left(x+5\right)}{2x-5}+\frac{x+3}{5-x}\)
\(=\left[\frac{\left(x-x+5\right)\left(x+x-5\right)}{x\left(x-5\right)\left(x+5\right)}\right].\frac{x\left(x+5\right)}{2x-5}+\frac{x+3}{5-x}\)
\(=\frac{5x.\left(2x-5\right)\left(x+5\right)}{x\left(x-5\right)\left(x+5\right)\left(2x-5\right)}+\frac{x+3}{5-x}\)
\(=\frac{5}{x-5}-\frac{x+3}{x-5}\)
\(=\frac{5-x-3}{x-5}\)
\(=\frac{-x+2}{x-5}\)
\(=-\frac{x-2}{x-5}\)
b: \(=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}\)
\(=\dfrac{\left(x+2\right)\left(x+3\right)+\left(x+1\right)\left(x+3\right)+\left(x+2\right)\left(x+1\right)}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)
\(=\dfrac{x^2+5x+6+x^2+4x+3+x^2+3x+2}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)
\(=\dfrac{3x^2+12x+11}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)
\(\left(\frac{3x-5}{x^2-5x}-\frac{x+5}{5x-25}\right):\frac{x^2-25}{x}\)
\(=\left[\frac{3x-5}{x\left(x-5\right)}-\frac{x+5}{5\left(x-5\right)}\right].\frac{x}{x^2-25}\)
\(=\left[\frac{\left(3x-5\right).5}{x\left(x-5\right).5}-\frac{\left(x+5\right).x}{5\left(x-5\right).x}\right].\frac{x}{x^2-25}\)
\(=\left[\frac{15x-25}{5x\left(x-5\right)}-\frac{x^2+5x}{5x\left(x-5\right)}\right].\frac{x}{\left(x-5\right)\left(x+5\right)}\)
\(=\frac{15x-25-x^2-5x}{5x\left(x-5\right)}.\frac{x}{\left(x-5\right)\left(x+5\right)}\)
\(=\frac{-x^2+10x-25}{5x\left(x-5\right)}.\frac{x}{\left(x-5\right)\left(x+5\right)}\)
\(=\frac{-\left(x-5\right)^2.x}{5x\left(x-5\right)\left(x-5\right)\left(x+5\right)}\)
\(=\frac{-1}{5\left(x+5\right)}\).