Question

5/x^2-5x - x/5x-25 simplify

Answer 1

$\bf \cfrac{5}{x^2-5x}-\cfrac{x}{5x-25}\implies \cfrac{5}{x(x-5)}-\cfrac{x}{5(x-5)}\impliedby \stackrel{LCD}{5x(x-5)} \\\\\\ \cfrac{25-x^2}{5x(x-5)}\implies \cfrac{5^2-x^2}{5x(x-5)}\implies \cfrac{\stackrel{\textit{difference of squares}}{(5-x)(5+x)}}{5x(x-5)} \\\\\\ \cfrac{\boxed{-\underline{(x-5)}}(5+x)}{5x\underline{(x-5)}}\implies \cfrac{-(5+x)}{5x}\implies \cfrac{-5-x}{5x}$