Rewrite the expression 7 x 2 + 7 x x 2 − 1 \frac{7x^2+7x}{x^2-1} into an equivalent expression having a denominator of x − 1 x-1 .

this problem, we are asked to rewrite the expression seven x squared plus seven x over x squared minus one into an equivalent expression having a denominator of x minus one. So we're trying to get a denominator of just x minus one from what we have right about here. So we have seven x squared plus seven x, and then in the denominator, we have x squared minus one. Now it's kinda tricky to see how to do this if we're just taking a look directly at this expression because everything is not factored at the moment. Usually, a straightforward way of dealing with any of these rational expressions is to factor first. So what I'm gonna start by doing is factoring the top. I can take a seven x in common out of each of these terms. That'll give me seven x on the outside of these parentheses. And dividing each of these terms by seven x will leave me with just an x there, then we'll have plus seven x over seven x will just be one. So I'm dividing that seven x out, bringing it to the outside of the parentheses. And then in the denominator, we have x squared minus one. X squared minus one is the same thing as x squared minus one squared. One squared is just equal to one. Now why would I write it like this? Well, notice this gives us a difference of squares. So x squared minus one squared can be factored into x plus one times x minus one. And notice I can just cancel the x plus one. So what that's gonna leave me with is seven x in the numerator, and then in the denominator, we'll have x minus one. Notice x minus one is the denominator we want it to have, so this is the solution to the problem.

Rewrite the expression 7 x 2 + 7 x x 2 − 1 \frac{7x^2+7x}{x^2-1} into an equivalent expression having a denominator of x − 1 x-1 .

7 x 2 + 7 x − 1 \frac{7x^2+7}{x-1}

7 x 2 − 7 x − 1 \frac{7x^2-7}{x-1}

8. Rational Expressions and Functions

Least Common Denominators

Intermediate Algebra

8. Rational Expressions and Functions

Least Common Denominators

Struggling with Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Rewrite the expression $\frac{7 x^{2} + 7 x}{x^{2} - 1}$ into an equivalent expression having a denominator of $x minus 1$ .

$\frac{7 x^{2}}{x - 1}$

$\frac{7 x^{2} + 7}{x - 1}$

$\frac{7 x}{x - 1}$

$\frac{7 x^{2} - 7}{x - 1}$

Verified step by step guidance

Start with the given expression: $\frac{7x^2 + 7x}{x^2 - 1}$.

Recognize that the denominator $x^2 - 1$ is a difference of squares, which factors as $x^2 - 1 = (x - 1)(x + 1)$.

Rewrite the expression using the factored denominator: $\frac{7x^2 + 7x}{(x - 1)(x + 1)}$.

Factor the numerator by taking out the common factor \$7x$: $7x^2 + 7x = 7x(x + 1)$, so the expression becomes $\frac{7x(x + 1)}{(x - 1)(x + 1)}$.

Cancel the common factor $(x + 1)$ from numerator and denominator to get an equivalent expression with denominator $x - 1$: $\frac{7x}{x - 1}$.

6:33m

Watch next

Master Least Common Denominators of Rational Expressions with a bite sized video explanation from Patrick Ford

Start learning

Struggling with Intermediate Algebra?

Rewrite the expression 7x2+7xx2−1\frac{7x^2+7x}{x^2-1} into an equivalent expression having a denominator of x−1x-1.

Watch next

Rewrite the expression $\frac{7 x^{2} + 7 x}{x^{2} - 1}$ into an equivalent expression having a denominator of $x minus 1$ .