Question

In the following exercises, simplify.

$\frac{\sqrt{7}}{\sqrt{y}+\sqrt{3}}$

Short answer

The answer is$\frac{\sqrt{7}\left(\sqrt{y}-\sqrt{3}\right)}{y-3}$

Step-by-step solution

Step 1. Given

The expression is$\frac{\sqrt{7}}{\sqrt{y}+\sqrt{3}}$

Step 2. Rationalize the denominators of the given expressions.

$$\begin{gathered} \frac{\sqrt{7}}{\sqrt{y}+\sqrt{3}} \\ =\frac{\sqrt{7}}{\sqrt{y}+\sqrt{3}}\times \frac{\sqrt{y}-\sqrt{3}}{\sqrt{y}-\sqrt{3}} \\ =\frac{\sqrt{7}\left(\sqrt{y}-\sqrt{3}\right)}{{\left(\sqrt{y}\right)}^2-{\left(\sqrt{3}\right)}^2} \\ =\frac{\sqrt{7}\left(\sqrt{y}-\sqrt{3}\right)}{y-3} \end{gathered}$$