Rationalize the denominator and simplify.
-$\frac{\sqrt{5}}{5 \sqrt{7}-\sqrt{5}}$
A) $\frac{\sqrt{35}+1}{36}$
B) $\frac{\sqrt{35}-1}{34}$
C) $\frac{\sqrt{7}+1}{34}$
D) $\frac{\sqrt{35}+1}{34}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $5\sqrt{7}+\sqrt{5}$. This results in $\frac{\sqrt{5}(5\sqrt{7}+\sqrt{5})}{(5\sqrt{7})^2-(\sqrt{5})^2}$. Simplifying gives $\frac{5\sqrt{35}+\sqrt{5}}{175-5} = \frac{5\sqrt{35}+\sqrt{5}}{170}$. Simplifying further, we get $\frac{\sqrt{35}+1}{34}$.

Rationalize the Denominator and Simplify 557−5\frac{\sqrt{5}}{5 \sqrt{7}-\sqrt{5}}57​−5​5​​ A) 35+136\frac{\sqrt{35}+1}{36}3635​+1​ B) 35−134\frac{\sqrt{35}-1}{34}3435​−1​ C) 7+134\frac{\sqrt{7}+1}{34}347​+1​ D) 35+134\frac{\sqrt{35}+1}{34}3435​+1​

Rationalize the Denominator and Simplify $\frac{\sqrt{5}}{5 \sqrt{7}-\sqrt{5}}$ A) $\frac{\sqrt{35}+1}{36}$ B) $\frac{\sqrt{35}-1}{34}$ C) $\frac{\sqrt{7}+1}{34}$ D) $\frac{\sqrt{35}+1}{34}$