The simplest form of the given problem is [tex]\frac{(x-1)(x-3)}{3(x+3)}[/tex]
Step-by-step explanation:
Given,
[tex]\frac{x^{2} +x-2}{x+3} .\frac{x-3}{3x+6}[/tex]
To find its simplified form.
First we will factorize [tex]x^{2} +x-2[/tex] by middle term factor formula.
Now,
[tex]x^{2} +x-2[/tex]
= [tex]x^{2} +2x-x-2[/tex]
= x(x+2)-1(x+2)
= (x+2)(x-1)
Putting this value into given problem we get,
[tex]\frac{x^{2} +x-2}{x+3} .\frac{x-3}{3x+6}[/tex]
= [tex]\frac{(x+2)(x-1)}{(x+3)} .\frac{x-3}{3(x+2)}[/tex] [ eliminating (x+2)]
= [tex]\frac{(x-1)(x-3)}{3(x+3)}[/tex]
This is the simplest form.
