Question

Show work and simplify the equation

Answer 1

Hello,

$if \ a \neq -3, a \neq 1, a \neq -5\\ \dfrac{2a^2+5a-3}{a^2+8a+15} * \dfrac{a^2+4a-5}{3a^2-a-2} \\ = \dfrac{(a+3)(2a-1)}{(a+5)(a+3)} * \dfrac{(a+5)(a-1)}{(a-1)(3a+2)} \\ = \dfrac{2a-1}{3a+2}$

explains:

1)
$a^2+4a-5=a^2+5a-a-5\\ =a(a+5)-(a+5)\\ =(a+5)(a-1)$

2)
$a^2+8a+15=a^2+5a+3a+15\\ =a(a+5)+3(a+5)\\ =(a+5)(a+3)$

3)
$a^2+4a-5=a^2+5a-a-5\\ =a(a+5)-(a+5)\\ =(a+5)(a-1)$

4)
$3a^2-a-2=3a^2-3a+2a-2\\ =3a(a-1)+2(a-1)\\ =(a-1)(3a+2)$