Answer
$\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}=\dfrac{1}{1-x^{2}}$
Work Step by Step
$\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}$
Evaluate the substraction of the two rational expressions:
$\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}=\dfrac{-8(1-x^{2})-7(x^{2}-1)}{(x^{2}-1)(1-x^{2})}=...$
Change the sign of the denominator and the sign of the fraction:
$...=-\dfrac{-8(1-x^{2})-7(x^{2}-1)}{(x^{2}-1)(x^{2}-1)}=-\dfrac{8(x^{2}-1)-7(x^{2}-1)}{(x^{2}-1)^{2}}=...$
$...=\dfrac{7(x^{2}-1)-8(x^{2}-1)}{(x^{2}-1)^{2}}=...$
Take out common factor $x^{2}-1$ from the numerator and simplify:
$...=\dfrac{(x^{2}-1)(7-8)}{(x^{2}-1)^{2}}=-\dfrac{1}{x^{2}-1}=\dfrac{1}{1-x^{2}}$