Question

Упростите выражение
$frac{5}{х-7} - frac{2}{х} - frac{3х+28}{ x^{2} -49}$

Answer 1

$=frac{5}{x-7}-frac{2}{x}-frac{3x+28}{x^{2}-7^2} =frac{5}{x-7}-frac{2}{x}-frac{3x+28}{(x-7)(x+7)}=$

$=frac{5*x*(x+7)}{(x-7)*x*(x+7)}-frac{2*(x-7)*(x+7)}{x*(x-7)*(x+7)}-frac{x*(3x+28)}{x*(x-7)(x+7)}=$

$=frac{5x(x+7)}{x(x-7)(x+7)}-frac{2(x^2-49)}{x*(x-7)*(x+7)}-frac{3x^2+28x}{x(x-7)(x+7)}=$

$=frac{5x^2+35x}{x(x-7)(x+7)}-frac{2x^2-98}{x*(x-7)*(x+7)}-frac{3x^2+28x}{x(x-7)(x+7)}=$

$=frac{5x^2+35x-(2x^2-98)-(3x^2+28x)}{x(x-7)(x+7)} =frac{5x^2+35x-2x^2+98-3x^2-28x}{x(x-7)(x+7)}=$

$=frac{5x^2-2x^2-3x^2+35x-28x+98}{x(x-7)(x+7)} =frac{7x+98}{x(x-7)(x+7)}= frac{7x^2+98}{x(x^2-49)}= frac{7x^2+98}{x^3-49x}$