There's f(x) = (2x+3)/(x+4)

Question

and g(x) = (4x-3)/(2-x)

Solve for x in f(g(x))

I tried this but I could not end up with the answer being x

Answer 1

f(g(x) = [2(4x-3)/(2-x) + 3]/[(4x-3)/(2-x) + 4]

= [(8x-6 + 6-3x)/(2-x)] / [(4x-3 + 8-4x)/(2-x)]

= [5x/(2-x)] / [5/(2-x)]
= [5x/(2-x)] [(2-x)/5]
= 5x/5
= x

Answer 2

thank you so much

Answer 3

welcome