Question

I know the right answer to this I just don't know how to get it, please help.

what is the product in simplest form? State any restrictions on the variable. (x^2+5x+6/x+4)*(x^2+x-12/x^2+x-2)



The right answer to this is (x+3)(x-3)/x-1
restrictions: -2, -4, 1

Answer 1

`\bf \cfrac{x^2+5x+6}{x+4}\cdot \cfrac{x^2+x-12}{x^2+x-2}\implies \cfrac{\underline{(x+2)}(x+3)}{\underline{x+4}}\cdot \cfrac{\underline{(x+4)}(x-3)}{\underline{(x+2)}(x-1)} \\\\\\ \cfrac{(x+3)(x-3)}{x-1}`

and yes, the restrictions are -4, -2 and 1.

the original expression has such restrictions because if ever "x" becomes one of those values, one of the denominators will turn to 0 making the fraction undefined.