Answer
a) Use the Distributive Property
b) Multiply the rational expression by the reciprocal of the polynomial, multiply the numerators and divide by the product of the denominators.
Work Step by Step
a) To multiply a rational expression by a polynomial, use the Distributive Property. That is, multiply the rational expression by each of the terms of the polynomial.
For example, the product of the rational expression $\frac{3}{x}$ and the polynomial expression $x+1$ is
$$\begin{aligned}
\frac{3}{x}(x+1)&=\frac{3}{x}(x)+\frac{3}{x}(1)
\\&=
3+\frac{3}{x}
.\end{aligned}$$
b) To divide a rational expression by a polynomial, multiply the rational expression by the reciprocal of the polynomial. Then multiply the numerators and divide by the product of the denominators.
For example, the quotient of the rational expression $\frac{3}{x}$ and the polynomial expression $x+1$ is
$$\begin{aligned}
\frac{3}{x}\div(x+1)&=\frac{3}{x}\times\frac{1}{x+1}
\\&=
\frac{3(1)}{x(x+1)}
\\&=
\frac{3}{x(x)+x(1)}
\\&=
\frac{3}{x^2+x}
.\end{aligned}$$
