a) \(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x^2}\left(ĐK:x\ne2;x\ne-2\right)\)
\(=\frac{4\left(x-2\right)+2\left(x+2\right)-\left(5x-6\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x-8+2x+4-5x+6}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{1}{x-2}\)
a ) \(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x^2}\)
\(=\frac{4}{x+2}+\frac{2}{x-2}+\frac{6-5x}{x^2-4}\)
\(=\frac{4\left(x-2\right)+\left(x+2\right)+6-5x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x-8+2x+4+6-5x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{1}{x-2}\)
\(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x^2}\)
\(=\frac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{5x-6}{\left(x-2\right)\left(2+x\right)}\)
\(=\frac{4x-8+2x+4-5x+6}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{1}{x-2}\)
