Rationalize the denominator and simplify.
-$\frac{\sqrt{7}}{\sqrt{5}+8}$
A) $\frac{\sqrt{35}-8 \sqrt{7}}{13}$
B) $\frac{3 \sqrt{35}+5 \sqrt{7}}{40}$
C) $\frac{-\sqrt{35}-8 \sqrt{7}}{59}$
D) $\frac{-\sqrt{35}+8 \sqrt{7}}{59}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $\sqrt{5} - 8$. This results in $\frac{\sqrt{7}(\sqrt{5} - 8)}{(\sqrt{5}+8)(\sqrt{5}-8)}$. The denominator becomes $5 - 64 = -59$. The numerator becomes $\sqrt{35} - 8\sqrt{7}$. Thus, the simplified expression is $\frac{-\sqrt{35} + 8\sqrt{7}}{59}$.

Rationalize the Denominator and Simplify 75+8\frac{\sqrt{7}}{\sqrt{5}+8}5​+87​​ A) 35−8713\frac{\sqrt{35}-8 \sqrt{7}}{13}1335​−87​​ B) 335+5740\frac{3 \sqrt{35}+5 \sqrt{7}}{40}40335​+57​​

Rationalize the Denominator and Simplify $\frac{\sqrt{7}}{\sqrt{5}+8}$ A) $\frac{\sqrt{35}-8 \sqrt{7}}{13}$ B) $\frac{3 \sqrt{35}+5 \sqrt{7}}{40}$