Simplify the algebraic fractions

Question

How could I simplify $\dfrac 8{x+5} - \dfrac 3{5-x}$? I know we should find the LCM for the denominators and then simplify, but this question is little confusing.

Answer 1

It is $$\frac{8}{x+5}-\frac{3}{5-x}=\frac{8(5-x)-3(5+x)}{(5+x)(5-x)}$$ for $$x\neq \pm5$$

Answer 2

For $x\ne\pm 5$, we have:

$$ \frac{8}{x+5} - \frac{3}{5-x}= $$

$$ =\frac{8(5-x)-3(5+x)}{(5+x)(5-x)}= $$

$$=\frac{40-8x-15-3x}{(5+x)(5-x)}=$$

$$=\frac{25-11x}{25-x^2}=$$

$$=\frac{11x-25}{x^2-25}.$$