CPM Homework Help : PC3 Problem 8-142

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

Step 1:

Multiply both sides of the equation 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:

Subtract $\sqrt{5}$ from both sides of the equation.

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

Step 4:

Simplify.