Simplify (5-8x)/( square root of -8x+5)

$\frac{(5 - 8 x)}{\sqrt{- 8 x + 5}}$

Step 1

Multiply $\frac{5 - 8 x}{\sqrt{- 8 x + 5}}$ by $\frac{\sqrt{- 8 x + 5}}{\sqrt{- 8 x + 5}}$ .

$\frac{5 - 8 x}{\sqrt{- 8 x + 5}} \cdot \frac{\sqrt{- 8 x + 5}}{\sqrt{- 8 x + 5}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{5 - 8 x}{\sqrt{- 8 x + 5}}$ by $\frac{\sqrt{- 8 x + 5}}{\sqrt{- 8 x + 5}}$ .

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{\sqrt{- 8 x + 5} \sqrt{- 8 x + 5}}$

Raise $\sqrt{- 8 x + 5}$ to the power of $1$ .

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{\sqrt{- 8 x + 5}}^{1} \sqrt{- 8 x + 5}}$

Raise $\sqrt{- 8 x + 5}$ to the power of $1$ .

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{\sqrt{- 8 x + 5}}^{1} {\sqrt{- 8 x + 5}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{\sqrt{- 8 x + 5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{\sqrt{- 8 x + 5}}^{2}}$

Rewrite ${\sqrt{- 8 x + 5}}^{2}$ as $- 8 x + 5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{- 8 x + 5}$ as ${(- 8 x + 5)}^{\frac{1}{2}}$ .

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{({(- 8 x + 5)}^{\frac{1}{2}})}^{2}}$

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

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{(- 8 x + 5)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{(- 8 x + 5)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{(- 8 x + 5)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{{(- 8 x + 5)}^{1}}$

Simplify.

$\frac{(5 - 8 x) \sqrt{- 8 x + 5}}{- 8 x + 5}$

Step 3

Cancel the common factor of $5 - 8 x$ and $- 8 x + 5$ .

Reorder terms.

$\frac{(- 8 x + 5) \sqrt{- 8 x + 5}}{- 8 x + 5}$

Cancel the common factor.

$\frac{(- 8 x + 5) \sqrt{- 8 x + 5}}{- 8 x + 5}$

Divide $\sqrt{- 8 x + 5}$ by $1$ .

$\sqrt{- 8 x + 5}$