Question

g(x)=2x^2-3x-2 and h(x) =3/(2-x). find the domain of (gh)(x) and simplify the expression?

Answer 1

so that looks like g times h

Answer 2

\[(gh)(x)=(2x^2-3x-2) \cdot \frac{3}{2-x}\]
the domain is all real numbers except with x=2

Answer 3

\[(gh)(x)=(2x^2-4x+1x-2) \cdot \frac{3}{-(x-2)}\]
\[=(2x(x-2)+1(x-2)) \cdot \frac{-3}{x-2}=(x-2)(2x+1)\cdot \frac{-3}{x-2}=-3(2x+1), x \neq 2\]

Answer 4

thank you for helping me!