How to simplify the following expression

g(x) = 4x^2 − 15x − 4 and h(x) = 5/(4-x)

find (gh)(x)

Thank You!

g(x) = 4x^2 − 15x − 4
h(x) = 5/(4-x)

g(h(x))
g(5/(4-x))
4(5/(4-x))^2 - 15(5/(4-x)) - 4

= 4((5)/(-x + 4))^2 - 15((5)/( -x + 4)) - 4

= (4*(25)/((( -x + 4))^2)) - 15((5)/((-x + 4))) - 4

= ((100)/(( -x + 4)^2)) - 15((5)/((-x + 4))) - 4

= (100)/(( -x + 4)^2) + (75)/((x - 4))*()/() - 4*(( -x + 4)^2)/(( -x + 4)^2)

= (100 + 75) - (4( -x + 4)^2))/(( - x + 4)^2)

= (-4x^2 + 32x + 111) / ((-x + 4)^2)