Simplify 7/(7+ square root of 14x)

$\frac{7}{7 + \sqrt{14 x}}$

Step 1

Multiply $\frac{7}{7 + \sqrt{14 x}}$ by $\frac{7 - \sqrt{14 x}}{7 - \sqrt{14 x}}$ .

$\frac{7}{7 + \sqrt{14 x}} \cdot \frac{7 - \sqrt{14 x}}{7 - \sqrt{14 x}}$

Step 2

Multiply $\frac{7}{7 + \sqrt{14 x}}$ by $\frac{7 - \sqrt{14 x}}{7 - \sqrt{14 x}}$ .

$\frac{7 (7 - \sqrt{14 x})}{(7 + \sqrt{14 x}) (7 - \sqrt{14 x})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (7 - \sqrt{14 x})}{49 - 7 \sqrt{14 x} + \sqrt{14 x} \cdot 7 - {\sqrt{14 x}}^{2}}$

Step 4

Simplify.

Rewrite ${\sqrt{14 x}}^{2}$ as $14 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14 x}$ as ${(14 x)}^{\frac{1}{2}}$ .

$\frac{7 (7 - \sqrt{14 x})}{49 - {({(14 x)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{7 (7 - \sqrt{14 x})}{49 - {(14 x)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{7 (7 - \sqrt{14 x})}{49 - {(14 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 (7 - \sqrt{14 x})}{49 - {(14 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{7 (7 - \sqrt{14 x})}{49 - {(14 x)}^{1}}$

Simplify.

$\frac{7 (7 - \sqrt{14 x})}{49 - (14 x)}$

Multiply $14$ by $- 1$ .

$\frac{7 (7 - \sqrt{14 x})}{49 - 14 x}$

Step 5

Cancel the common factors.

Factor $7$ out of $49$ .

$\frac{7 (7 - \sqrt{14 x})}{7 (7) - 14 x}$

Factor $7$ out of $- 14 x$ .

$\frac{7 (7 - \sqrt{14 x})}{7 (7) + 7 (- 2 x)}$

Factor $7$ out of $7 (7) + 7 (- 2 x)$ .

$\frac{7 (7 - \sqrt{14 x})}{7 (7 - 2 x)}$

Cancel the common factor.

$\frac{7 (7 - \sqrt{14 x})}{7 (7 - 2 x)}$

Rewrite the expression.

$\frac{7 - \sqrt{14 x}}{7 - 2 x}$