Tính x 2 − 36 2 x + 10 . 3 6 − x

$\begin{array}{l}A=\frac{1}{x}+\frac{1}{x+5}-\frac{5-x}{x(x+5)}=\frac{x+5}{x\left(x-5\right)}+\frac{x}{x\left(x-5\right)}+\frac{x-5}{x\left(x-5\right)}\\ =\frac{x+5+x+x-5}{x\left(x-5\right)}=\frac{3x}{x\left(x-5\right)}=\frac{3}{x-5}=B\end{array}$

$\frac{x}{x+10}-\frac{-10}{x+10}=\frac{x}{x+10}+\frac{10}{x+10}=\frac{x+10}{x+10}=1$

$\frac{x^2-10x}{x^2-25}-\frac{25}{25-x^2}=\frac{x^2-10x}{x^2-25}+\frac{25}{x^2-25}=\frac{x^2-10x+25}{x^2-25}=\frac{{\left(x-5\right)}^2}{\left(x-5\right)\left(x+5\right)}=\frac{x-5}{x+5}.$

$\frac{x+1}{2x+6}+\frac{2x+3}{x^2+3x}=\frac{x\left(x+1\right)}{2x\left(x+3\right)}+\frac{2\left(2x+3\right)}{2x\left(x+3\right)}=\frac{x^2+x+4x+6}{2x\left(x+3\right)}=\frac{x^2+5x+6}{2x\left(x+3\right)}=\frac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\frac{x+2}{2x}$

$\frac{x}{x-2y}+\frac{x}{x+2y}-\frac{4xy}{x^2-4y^2}=\frac{x\left(x+2y\right)+x\left(x-2y\right)-4xy}{x^2-4y^2}=\frac{2x^2-4xy}{x^2-4y^2}=\frac{2x\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}=\frac{2x}{x+2y}$