Question

Show work and simplify the equation

Answer 1

Hello,


`if \ a \\eq -3, a \\eq 1, a \\eq -5\\ (2a^2+5a-3)/(a^2+8a+15) * (a^2+4a-5)/(3a^2-a-2) \\ = ((a+3)(2a-1))/((a+5)(a+3)) * ((a+5)(a-1))/((a-1)(3a+2)) \\ = (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)`