Question

tính

\[ c) \frac{2x}{x^2-4} - \left( \frac{2}{x+5} + \frac{3-x}{x+1} \right) + \left[ \frac{2}{x+5} - \left( \frac{4}{x^2-4} + \frac{x-3}{x+1} \right) \right] \]

\[ d) \frac{2x}{x^2+2xy} + \frac{y}{xy-2y^2} + \frac{4}{x^2-4y^2} \]

Answer 1

c) \(...=\dfrac{2x}{x^2-4}-\dfrac{4}{x^2-4}-\dfrac{2}{x+5}+\dfrac{2}{x+5}-\dfrac{3-x}{x+1}-\dfrac{x-3}{x+1}\left(x\ne\left\{-5;-2;-1;2\right\}\right)\)

\(=\dfrac{2x-4}{x^2-4}+\dfrac{-2+2}{x+5}+\dfrac{x-3-x+3}{x+1}\)

\(=\dfrac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2}{x+2}\)

d) \(...=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\left(x\ne\pm2y\right)\)

\(=\dfrac{2}{x+2y}+\dfrac{1}{x-2y}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2\left(x-2y\right)+\left(x+2y\right)+4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2x-4y+x+2y+4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{3x-2y+4}{\left(x-2y\right)\left(x+2y\right)}\)