Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 10 - \sqrt { 7 } } { 10 + \sqrt { 7 } }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 10 - \sqrt { 7 } } { 10 + \sqrt { 7 } }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $10 - \sqrt{7}$. This results in $\frac{(10 - \sqrt{7})^2}{(10 + \sqrt{7})(10 - \sqrt{7})}$. Simplifying, the denominator becomes $10^2 - (\sqrt{7})^2 = 100 - 7 = 93$, and the numerator becomes $10^2 - 2 \cdot 10 \cdot \sqrt{7} + 7 = 107 - 20\sqrt{7}$. Therefore, the simplified form is $\frac { 107 - 20 \sqrt { 7 } } { 93 }$.

Rationalize the Denominator and Simplify 10−710+7\frac { 10 - \sqrt { 7 } } { 10 + \sqrt { 7 } }10+7​10−7​​

Rationalize the Denominator and Simplify $\frac { 10 - \sqrt { 7 } } { 10 + \sqrt { 7 } }$