Question

Упростите выражение
(x^2 - 25) (5/x-5 - 4/x+5) - 18.

Answer 1

(x²-25)*(5x+25-4x+20)/(x²-25) -18==x+40-18=x+22

Answer 2

$( x^{2} -25)( \frac{5}{x-5} - \frac{4}{x+5} )-18= x+27\\ \\ 1) \frac{5}{x-5} - \frac{4}{x+5} = \frac{5(x+5)}{(x-5)(x+5)} - \frac{4(x-5)}{(x-5)(x+5)} = \\ \\ = \frac{5x+25}{ x^{2} -25} - \frac{4x-20}{ x^{2} -25} = \frac{5x+25-4x+20}{ x^{2} -25} = \frac{x+45}{ x^{2} -25} \\ \\ 2) x^{2} -25* \frac{x+45}{ x^{2} -25} =x+45\\\\3)x+45-18=x+27$