Algebra Examples

$\frac{7 x}{3 - \sqrt{2}}$

Step 1

Multiply $\frac{7 x}{3 - \sqrt{2}}$ by $\frac{3 + \sqrt{2}}{3 + \sqrt{2}}$ .

$\frac{7 x}{3 - \sqrt{2}} \cdot \frac{3 + \sqrt{2}}{3 + \sqrt{2}}$

Step 2

Multiply $\frac{7 x}{3 - \sqrt{2}}$ by $\frac{3 + \sqrt{2}}{3 + \sqrt{2}}$ .

$\frac{7 x (3 + \sqrt{2})}{(3 - \sqrt{2}) (3 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 x (3 + \sqrt{2})}{9 + 3 \sqrt{2} - 3 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{7 x (3 + \sqrt{2})}{7}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$\frac{7 x (3 + \sqrt{2})}{7}$

Step 5.2

Divide $x (3 + \sqrt{2})$ by $1$ .

$x (3 + \sqrt{2})$

Step 6

Apply the distributive property.

$x \cdot 3 + x \sqrt{2}$

Step 7

Move $3$ to the left of $x$ .

$3 x + x \sqrt{2}$