Giải thích các bước giải:

a.Ta có:

$\dfrac6{7-x}+\dfrac{-4}x+\dfrac6{x-7}+\dfrac2{x-2}+\dfrac4{x}+\dfrac{-5}{x+2}$

$=-\dfrac6{x-7}-\dfrac4x+\dfrac6{x-7}+\dfrac2{x-2}+\dfrac4x-\dfrac5{x+2}$

$=(\dfrac6{x-7}-\dfrac6{x-7})+(\dfrac4x-\dfrac4x)+(\dfrac2{x-2}-\dfrac5{x+2})$ 

$=0+\dfrac{2\left(x+2\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}$

$=\dfrac{-3x+14}{\left(x-2\right)\left(x+2\right)}$

b.Ta có:

$\dfrac{x-1}{x^2-4}-\dfrac1{x+2}+\dfrac{x+2}x+\dfrac1{x+2}-\dfrac{x+2}x-\dfrac3{x-2}$

$=(\dfrac{x-1}{x^2-4}-\dfrac3{x-2})+(\dfrac1{x+2}-\dfrac1{x+2})+(\dfrac{x+2}x-\dfrac{x+2}x)$

$=\dfrac{x-1-3\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}$

$=\dfrac{-2x-7}{\left(x+2\right)\left(x-2\right)}$