Question

"TexFormula1" title="\frac{a^{2}-1}{2-5a} times \frac{15a-6}{a^{2}+5a-6}" alt="\frac{a^{2}-1}{2-5a} times \frac{15a-6}{a^{2}+5a-6}" align="absmiddle" class="latex-formula">
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Answer 1

$\bf \cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\\\\ -----------------------------\\\\ recall\quad \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ thus\quad a^2-1\iff a^2-1^2\implies (a-1)(a+1) \\\\\\ now\quad a^2+5a-6\implies (a+6)(a-1)\\\\ -----------------------------\\\\ thus \\\\\\ \cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}\times \cfrac{3(5a-2)}{(a+6)(a-1)}\\\\ -----------------------------$

$\bf now\quad 3(5a-2) \iff -3(2-5a)\\\\ -----------------------------\\\\ thus \\\\\\ \cfrac{\underline{(a-1)}(a+1)}{\underline{2-5a}}\times \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}$