Cho biểu thức A= 4x/x^2 - 25 + 3/x+5 - 2/x-5 (với x khác +- 5) 1. Rút gọn biểu thức A.

Hướng dẫn giải

ĐKXĐ:$\left\{\begin{array}{c}x-5\ne 0\\ x+5\ne 0\end{array}\right.\iff \left\{\begin{array}{c}x\ne 5\\ x\ne -5\end{array}\right.$

1.$A=\frac{4x}{x^2-25}+\frac{3}{x+5}-\frac{2}{x-5}$

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

$=\frac{4x}{\left(x-5\right)\left(x+5\right)}+\frac{3x-15}{\left(x-5\right)\left(x+5\right)}-\frac{2x+10}{\left(x-5\right)\left(x+5\right)}$

$=\frac{4x+3x-15-2x-10}{\left(x-5\right)\left(x+5\right)}=\frac{5x-25}{\left(x-5\right)\left(x+5\right)}$

$=\frac{5x-25}{\left(x-5\right)\left(x+5\right)}=\frac{5\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}$

 $=\frac{5}{x+5}$với x ¹ ± 5