$\frac{a^{2}-b^{2}-2 b c-c^{2}}{a^{2}+b^{2}+2 a b-c^{2}}$ is equivalent to
(a)$\frac{a-b+c}{a+b+c}$
(b)$\frac{a-b-c}{a-b+c}$
(c)$\frac{a-b-c}{a+b-c}$
(d)$\frac{a+b+c}{a-b+c}$
Answer
Answer (as printed): C
Explanation
$\frac{a^{2}-b^{2}-2 b c-c^{2}}{a^{2}+b^{2}+2 a b-c^{2}}=\frac{a^{2}-\left(b^{2}+2 b c+c^{2}\right)}{\left(a^{2}+b^{2}+2 a b\right)-c^{2}}=\frac{a^{2}-(b+c)^{2}}{(a+b)^{2}-c^{2}}$ $$=\frac{(a+b+c)(a-b-c)}{(a+b+c)(a+b-c)}=\frac{a-b-c}{a+b-c} .$$
Explanation as extracted from the printed page; notation may be imperfect.