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

• A. $\frac{7x^2}{x-1}$
• B. $\frac{7x^2+7}{x-1}$
• C. $\frac{7x}{x-1}$
• D. $\frac{7x^2-7}{x-1}$

Answer: (C)

Verified step by step guidance

1. Start with the given expression: \(\frac{7x^2 + 7x}{x^2 - 1}\).
2. Recognize that the denominator \(x^2 - 1\) is a difference of squares, which factors as \(x^2 - 1 = (x - 1)(x + 1)\).
3. Rewrite the expression using the factored denominator: \(\frac{7x^2 + 7x}{(x - 1)(x + 1)}\).
4. Factor the numerator by taking out the common factor \$7x\(: \)7x^2 + 7x = 7x(x + 1)$, so the expression becomes \(\frac{7x(x + 1)}{(x - 1)(x + 1)}\).
5. Cancel the common factor \((x + 1)\) from numerator and denominator to get an equivalent expression with denominator \(x - 1\): \(\frac{7x}{x - 1}\).