(a^(2)-1)/(2-5a) times (15a-6)/(a^(2)+5a-6) click on answer to see full problem

Question

`(a^(2)-1)/(2-5a) times (15a-6)/(a^(2)+5a-6)`

click on answer to see full problem

Answer 1

`\bf \cfrac{a^2-1}{2-5a}* \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}* \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}* \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}}* \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}`