Final answer to the problem
$f\left(x\right)=\frac{-1}{1-x^2}$
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Apply the formula: $\left(a+b\right)\left(a+c\right)$$=a^2-b^2$, where $a=1$, $b=x$, $c=-x$, $a+c=x+1$ and $a+b=1-x$
$f\left(x\right)=\frac{-1}{1-x^2}$
Final answer to the problem
$f\left(x\right)=\frac{-1}{1-x^2}$
