Question

how do i find g(f(x) with these f(x) = x-7÷x+3 and g(x) = -3x-7÷x-1

Answer 1

You would want to put the function of f(x) into all of the x in g(x), so that
$-3(x-7/x+3)-7/(x-7/x+3)-1$
Then you simplify and convert the constants into fractions of same value.
$((-3x+21/x+3)-(7x+21/x+3))/(x-7/x+3)-(x+3/x+3)$
simplify
$(-10x/x+3)/(-10/x+3)$