Question

I have the picture of the equation.

find (f+g)(x)=
find (f-g)(x)=
find (f·g)(x)=

Answer 1

`f(x)=(5x+7)/(7x-5),\ g(x)=(8x)/(7x-5)\\\\(f+g)(x)=f(x)+g(x)=(5x+7)/(7x-5)+(8x)/(7x-5)=(5x+7+8x)/(7x-5)=(13x+7)/(7x-5)\\\\(f-g)(x)=f(x)-g(x)=(5x+7)/(7x-5)-(8x)/(7x-5)=(5x+7-8x)/(7x-5)=(-3x+7)/(7x-5)\\\\(f\cdot g)(x)=f(x)\cdot g(x)=(5x+7)/(7x-5)\cdot(8x)/(7x-5)=((5x+7)(8x))/((7x-5)(7x-5))\\\\=(40x^2+56x)/((7x)(7x)+(7x)(-5)+(-5)(7x)+(-5)(-5))=(40x^2+56x)/(49x^2-70x+25)`