Q. 272 - Intermediate Algebra

Question

In the following exercises, simplify. 

$\frac{7}{2-\sqrt{6}}$

Step-by-Step Solution

Answer

The simplified form is $-\frac{7\left(2+\sqrt{6}\right)}{2}$.

Step 1. Given information.

The given expression is,

$\frac{7}{2-\sqrt{6}}$.

Step 2. Simplifying.

Now, to rationalize we will multiply the numerator and denominator by the conjugate of the denominator and simplify. 

$$\begin{gathered} \frac{7}{2-\sqrt{6}}=\frac{7\left(2+\sqrt{6}\right)}{\left(2-\sqrt{6}\right)\left(2+\sqrt{6}\right)} \\ =\frac{7\left(2+\sqrt{6}\right)}{2^4-{\left(\sqrt{6}\right)}^2} \\ =\frac{7\left(2+\sqrt{6}\right)}{4-6} \\ =-\frac{7\left(2+\sqrt{6}\right)}{2} \end{gathered}$$