a^2 - b^2 - 2bc - c^2a^2 + b^2 + 2ab - c^2 is equivalent to = ?

Answer: Option C

$$\begin{array}{rl}& \frac{a^2-b^2-2bc-c^2}{a^2+b^2+2ab-c^2}\\ & =\frac{a^2-(b^2+2bc+c^2)}{(a^2+b^2+2ab)-c^2}\\ & =\frac{a^2-{(b+c)}^2}{{(a+b)}^2-c^2}\\ & =\frac{\left(a+b+c\right)\left(a-b-c\right)}{\left(a+b+c\right)\left(a+b-c\right)}\\ & =\frac{a-b-c}{a+b-c}\end{array}$$