Simplify 4/( square root of 5a)-2/( square root of 5a)-(7 square root of 5a)/(5a)

$\frac{4}{\sqrt{5 a}} - \frac{2}{\sqrt{5 a}} - \frac{7 \sqrt{5 a}}{5 a}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{4 - 2}{\sqrt{5 a}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Subtract $2$ from $4$ .

$\frac{2}{\sqrt{5 a}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Simplify each term.

Multiply $\frac{2}{\sqrt{5 a}}$ by $\frac{\sqrt{5 a}}{\sqrt{5 a}}$ .

$\frac{2}{\sqrt{5 a}} \cdot \frac{\sqrt{5 a}}{\sqrt{5 a}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{5 a}}$ by $\frac{\sqrt{5 a}}{\sqrt{5 a}}$ .

$\frac{2 \sqrt{5 a}}{\sqrt{5 a} \sqrt{5 a}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Raise $\sqrt{5 a}$ to the power of $1$ .

$\frac{2 \sqrt{5 a}}{{\sqrt{5 a}}^{1} \sqrt{5 a}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Raise $\sqrt{5 a}$ to the power of $1$ .

$\frac{2 \sqrt{5 a}}{{\sqrt{5 a}}^{1} {\sqrt{5 a}}^{1}} + \frac{- 7 \sqrt{5 a}}{5 a}$

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

$\frac{2 \sqrt{5 a}}{{\sqrt{5 a}}^{1 + 1}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Add $1$ and $1$ .

$\frac{2 \sqrt{5 a}}{{\sqrt{5 a}}^{2}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Rewrite ${\sqrt{5 a}}^{2}$ as $5 a$ .

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

$\frac{2 \sqrt{5 a}}{{({(5 a)}^{\frac{1}{2}})}^{2}} + \frac{- 7 \sqrt{5 a}}{5 a}$

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

$\frac{2 \sqrt{5 a}}{{(5 a)}^{\frac{1}{2} \cdot 2}} + \frac{- 7 \sqrt{5 a}}{5 a}$

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

$\frac{2 \sqrt{5 a}}{{(5 a)}^{\frac{2}{2}}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{5 a}}{{(5 a)}^{\frac{2}{2}}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Rewrite the expression.

$\frac{2 \sqrt{5 a}}{{(5 a)}^{1}} + \frac{- 7 \sqrt{5 a}}{5 a}$

Simplify.

$\frac{2 \sqrt{5 a}}{5 a} + \frac{- 7 \sqrt{5 a}}{5 a}$

Move the negative in front of the fraction.

$\frac{2 \sqrt{5 a}}{5 a} - \frac{7 \sqrt{5 a}}{5 a}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{2 \sqrt{5 a} - 7 \sqrt{5 a}}{5 a}$

Subtract $7 \sqrt{5 a}$ from $2 \sqrt{5 a}$ .

$\frac{- 5 \sqrt{5 a}}{5 a}$

Cancel the common factor of $- 5$ and $5$ .

Factor $5$ out of $- 5 \sqrt{5 a}$ .

$\frac{5 (- \sqrt{5 a})}{5 a}$

Cancel the common factors.

Factor $5$ out of $5 a$ .

$\frac{5 (- \sqrt{5 a})}{5 (a)}$

Cancel the common factor.

$\frac{5 (- \sqrt{5 a})}{5 a}$

Rewrite the expression.

$\frac{- \sqrt{5 a}}{a}$

Move the negative in front of the fraction.

$- \frac{\sqrt{5 a}}{a}$

Simplify 4/( square root of 5a)-2/( square root of 5a)-(7 square root of 5a)/(5a)

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