Chứng minh đẳng thức :
a)\(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)=\frac{3}{3-x}\)
b) \([\frac{2}{3x}-\frac{2}{x+1}.\left(\frac{x+1}{3x}-x-1\right)]:\frac{x-1}{x}=\frac{2x}{x-1}\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) \(\frac{x^2+2x-3}{x^2+x-6}\)
\(=\frac{x^2+3x-x-3}{x^2-2x+3x-6}\)
\(=\frac{x\left(x+3\right)-\left(x+3\right)}{x\left(x-2\right)+3\left(x-2\right)}\)
\(=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\)
\(=\frac{x-1}{x-2}\)
b) \(\frac{2x^2+2x+2}{x^2+6x-7}\)
\(=\frac{2\left(x^2+x+1\right)}{x^2+7x-x-7}\)
\(cogidosaisai?\)
a) \(\frac{x^2}{x-1}-\frac{2x}{x-1}+\frac{1}{x-1}\)
\(=\frac{x^2-2x+1}{x-1}\)
\(=\frac{\left(x-1\right)^2}{x-1}=x-1\)
b) \(\left(\frac{1}{1-2x}+\frac{1}{1+2x}\right):\frac{1}{1-2x}\)
\(=\left(\frac{1+2x}{\left(1-2x\right)\left(1+2x\right)}+\frac{1-2x}{\left(1+2x\right)\left(1-2x\right)}\right):\frac{1}{1-2x}\)
\(=\frac{2}{\left(1-2x\right)\left(1+2x\right)}.\left(1-2x\right)\)
\(=\frac{2}{1+2x}\)
\(a.=\frac{4x\left(x^2-2x+1\right)}{x^2-1x-5x+5}\)
\(=\frac{4x\left(x-1\right)^2}{x\left(x-1\right)-5\left(x-1\right)}\)
\(=\frac{4x\left(x-1\right)^2}{\left(x-5\right)\left(x-1\right)}\)
\(=\frac{4x\left(x-1\right)}{x-5}\)
b) \(\frac{4x^3-64x}{x^2-7x+12}\)
\(=\frac{4x\left(x^2-16\right)}{x^2-3x-4x+12}\)
\(=\frac{4x\left(x+4\right)\left(x-4\right)}{x\left(x-3\right)-4\left(x-3\right)}\)
\(=\frac{4x\left(x+4\right)\left(x-4\right)}{\left(x-4\right)\left(x-3\right)}\)
\(=\frac{4x\left(x+4\right)}{x-3}=\frac{4x^2+16x}{x-3}\)
c) \(\frac{x^2-6x+8}{x^3-8}\)
\(=\frac{x^2-2x-4x+8}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\frac{x\left(x-2\right)-4\left(x-2\right)}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\frac{\left(x-4\right)\left(x-2\right)}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\frac{x-4}{x^2+2x+4}\)
\(=xy+3y-2x\left(x+3\right)\)
\(=\left(x+3\right)y-2x\left(x+3\right)\)
\(=\left(x+3\right)\left(y-2x\right)\)
b) \(\left[\frac{2}{3x}-\frac{2}{x+1}.\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2}{x+1}.\left(\frac{x+1}{3x}-\left(x+1\right)\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2}{x+1}.\left(x+1\right)\left(\frac{1}{3x}-1\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-2\left(\frac{1}{3x}-1\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2}{3x}+2\right]:\frac{x-1}{x}\)
\(=2.\frac{x}{x-1}=\frac{2x}{x-1}\left(đpcm\right)\)
a) \(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)
\(=\left(\frac{9}{x\left(x^2-9\right)}+\frac{1}{x+3}\right):\left(\frac{x-3}{x\left(x+3\right)}-\frac{x}{3\left(x+3\right)}\right)\)
\(=\left(\frac{9}{x\left(x+3\right)\left(x-3\right)}+\frac{x^2-3x}{x\left(x+3\right)\left(x-3\right)}\right)\)
\(:\left(\frac{3x-9}{3x\left(x+3\right)}-\frac{x^2}{3x\left(x+3\right)}\right)\)
\(=\frac{x^2-3x+9}{x\left(x+3\right)\left(x-3\right)}:\frac{-x^2+3x-9}{3x\left(x+3\right)}\)
\(=\frac{x^2-3x+9}{x\left(x+3\right)\left(x-3\right)}.\frac{3x\left(x+3\right)}{-x^2+3x-9}\)
\(=\frac{x^2-3x+9}{x-3}.\frac{3}{x^2+3x-9}\)
\(=\frac{x^2-3x+9}{3-x}.\frac{3}{x^2-3x+9}\)
\(=\frac{3}{3-x}\left(đpcm\right)\)