Question

guided practice
to divide rational expressions:
step 1
factor the numerator and denominator.
step 2
identify restrictions on the variable.
step 3
multiply by the reciprocal of the divisor.
step 4
rational expressions
step 3
type the numerator in the top blank and the denominator in the bottom blank and then click or tap done.
what is the reciprocal of \\(\frac{x + 1}{3(x - 4)}\\)? be sure to include parentheses, if needed.

Explanation:

Step1: Recall the definition of reciprocal

The reciprocal of a fraction $\frac{a}{b}$ (where $a
eq0$ and $b
eq0$) is $\frac{b}{a}$.
For the rational expression $\frac{x + 1}{3(x - 4)}$, we want to find its reciprocal.

Step2: Apply the reciprocal definition

Using the definition of reciprocal, we swap the numerator and the denominator of the fraction $\frac{x + 1}{3(x - 4)}$.
So the numerator becomes $3(x - 4)$ and the denominator becomes $x + 1$.

Answer:

The reciprocal of $\frac{x + 1}{3(x - 4)}$ is $\frac{3(x - 4)}{x + 1}$. So the numerator (top blank) is $3(x - 4)$ and the denominator (bottom blank) is $x + 1$.