CPM Homework Help : AC Problem 9-13

Solve exactly for $x$ : $\frac { \sqrt { 5 } + x } { \sqrt { 5 } + \sqrt { 2 } }=3$

Step 1:

$\text{Multiply both sides by }\sqrt{5} + \sqrt{2}.$

$\sqrt{5} + \textit{x} = 3(\sqrt{5} + \sqrt{2})$

Step 2:

Distribute.

$\sqrt{5} + \textit{x} = 3\sqrt{5} + 3\sqrt{2}$

Step 3:

$\text{Subtract }\sqrt{5}\text{ from both sides.}$

$x = 3\sqrt{5} + 3\sqrt{2} - \sqrt{5}$

Step 4:

Simplify.

Answer:

$x = 2\sqrt{5} + 3\sqrt{2}$