\(\frac{x+2}{x-2}-\frac{x-2}{x+2}=\frac{4x^2}{x^2-4}\)
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2 tháng 8 2018
\(C=\left[\frac{x^2.\left(x^2-4\right)+4x^2}{x^2-4}\right].\left[\frac{x}{2.\left(x-2\right)}+\frac{2-2x}{x.\left(x^2-4\right)}.\frac{x^2-4}{x-2}\right]\)
\(C=\frac{x^4-4x^2+4x^2}{x^2-4}.\left[\frac{x}{2.\left(x-2\right)}+\frac{2-2x}{x\left(x-2\right)}\right]\)
\(C=\frac{x^4}{x^2-4}.\left[\frac{x^2}{2x.\left(x-2\right)}+\frac{\left(2-2x\right).2}{2x.\left(x-2\right)}\right]\)
\(C=\frac{x^4}{x^2-4}.\left[\frac{x^2+4-4x}{2x.\left(x-2\right)}\right]\)
\(C=\frac{x^4}{x^2-4}.\frac{\left(x-2\right)^2}{2x.\left(x-2\right)}\)
\(C=\frac{x^4}{\left(x-2\right).\left(x+2\right)}.\frac{\left(x-2\right).\left(x-2\right)}{2x.\left(x-2\right)}\)
\(C=\frac{x^3}{\left(x+2\right).2}\)
PA
21 tháng 10 2016
\(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}\times\left(\frac{2}{2-x}-\frac{8}{8+x^3}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{4-4x+x^2}{4x^2}\times\left(\frac{2}{2-x}-\frac{8}{\left(2+x\right)\left(4-2x+x^2\right)}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{\left(2-x\right)^2}{4x^2}\times\left(\frac{2\left(2+x\right)}{\left(2+x\right)\left(2+x\right)}-\frac{8}{\left(2+x\right)\left(2-x\right)}\right)\)
\(=\frac{\left(2+x\right)\left(2-x\right)}{4x^2}\times\frac{4+2x-8}{\left(2+x\right)\left(2-x\right)}\)
\(=\frac{2\left(2+x-4\right)}{4x^2}\)
\(=\frac{x-2}{2x^2}\)
\(\frac{x+2}{x-2}-\frac{x-2}{x+2}=\frac{4x^2}{x^2-4}\)ĐKXĐ : \(x\ne\pm2\)
\(\Leftrightarrow\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}=\frac{4x^2}{\left(x+2\right)\left(x-2\right)}\)
\(\Leftrightarrow\frac{x^2+4x+4-x^2+4x-4}{\left(x+2\right)\left(x-2\right)}=\frac{4x^2}{\left(x+2\right)\left(x-2\right)}\)
\(\Leftrightarrow8x=4x^2\)
\(\Leftrightarrow4x^2-8x=0\)
\(\Leftrightarrow4x\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\left(chon\right)\\x=2\left(loai\right)\end{cases}}\)
Vậy....