Question

For given functions f and g find formulas for a)f o g and b)g o f. Simplify results as much as possible. f(x)= x+7/x-13 , g(x)= 1/x+1

Answer 1

I will assume that you meant
f(x) = (x+7)/(x-13) and g(x) = 1/(x+1)

Those brackets are very critical in this text format.

f o g = f( g(x) )
= (1/(x+1) + 7)/(1/(x+1) - 13)
multiply top and bottom by x+1
= (1 + 7(x+1))/)1 - 13(x+1) )
= (7x + 8)/(-13x - 12)
or
-(7x+8)/(13x - 12)

g o f = g( f(x) )
= .....
follow the same steps I used in the first example