Answer
See an explanation
Work Step by Step
$f(x)=\frac{2x+3}{3x-2},$ $g(x)=\frac{4x}{3x-2}$
a.$(f+g)(x)=\frac{2x+3}{3x-2}+\frac{4x}{3x-2}=\frac{6x+3}{3x-2}$
for all ${ x|x \in \mathbb{R} \ne 2/3}$
b.$(f-g)(x)=\frac{2x+3}{3x-2}-\frac{4x}{3x-2}=\frac{-2x+3}{3x-2}$
for all ${ x|x \in \mathbb{R} \ne 2/3}$
c. $(f \times g)(x)=\frac{(2x+3)(4x)}{(3x-2)(3x-2)}=\frac{8x^2+12x}{9x^2-12x+4}$
for all ${ x|x \in \mathbb{R} \ne 2/3}$
d. $(f/g)(x)=\frac{2x+3}{4x}$
for all ${ x|x \in \mathbb{R} \ne \{2/3, 0 \}}$
e. $(f+g)(3)=3$
f. $(f-g)(4)=-\frac{1}{2}$
g. $(f\times g)(2)=14$
h. $(f/g)(1)=\frac{5}{4}$
