Giải thích các bước giải:
a.ĐKXĐ: $x\ne \pm2$
Ta có:
$\dfrac{x+1}{x-2}+\dfrac{x-1}{x+2}=\dfrac{2(x^2+2)}{x^2-4}$
$\to \dfrac{x+1}{x-2}+\dfrac{x-1}{x+2}=\dfrac{2(x^2+2)}{(x-2)(x+2)}$
$\to\left(x+1\right)\left(x+2\right)+\left(x-1\right)\left(x-2\right)=2\left(x^2+2\right)$
$\to 2x^2+4=2x^2+4$ luôn đúng
$\to$Phương trình có nghiệm với mọi $x\in R, x\ne\pm2$
b.ĐKXĐ: $x\ne \dfrac72$
Ta có:
$(2x+3)\cdot (\dfrac{3x+8}{2-7x}+1)=(x-5)(\dfrac{3x+2}{2-7x}+1)$
$\to (2x+3)\cdot \dfrac{3x+8+2-7x}{2-7x}=(x-5)\cdot \dfrac{3x+2+2-7x}{2-7x}$
$\to (2x+3)\cdot \dfrac{10-4x}{2-7x}=(x-5)\cdot \dfrac{4-4x}{2-7x}$
$\to (2x+3)(10-4x)=(x-5)\cdot (4-4x)$
$\to (2x+3)(5-2x)=(x-5)\cdot (2-2x)$
$\to -4x^2+4x+15=-2x^2+12x-10$
$\to -2x^2-8x+25=0$
$\to x=\dfrac{-4\pm\sqrt{66}}{2}$
