Basic Math Examples

$(2 m + 1) \div \sqrt{- m + 1}$

Step 1

Rewrite the division as a fraction.

$\frac{2 m + 1}{\sqrt{- m + 1}}$

Step 2

Multiply $\frac{2 m + 1}{\sqrt{- m + 1}}$ by $\frac{\sqrt{- m + 1}}{\sqrt{- m + 1}}$ .

$\frac{2 m + 1}{\sqrt{- m + 1}} \cdot \frac{\sqrt{- m + 1}}{\sqrt{- m + 1}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{2 m + 1}{\sqrt{- m + 1}}$ by $\frac{\sqrt{- m + 1}}{\sqrt{- m + 1}}$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{\sqrt{- m + 1} \sqrt{- m + 1}}$

Step 3.2

Raise $\sqrt{- m + 1}$ to the power of $1$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{{\sqrt{- m + 1}}^{1} \sqrt{- m + 1}}$

Step 3.3

Raise $\sqrt{- m + 1}$ to the power of $1$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{{\sqrt{- m + 1}}^{1} {\sqrt{- m + 1}}^{1}}$

Step 3.4

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

$\frac{(2 m + 1) \sqrt{- m + 1}}{{\sqrt{- m + 1}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{{\sqrt{- m + 1}}^{2}}$

Step 3.6

Rewrite ${\sqrt{- m + 1}}^{2}$ as $- m + 1$ .

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Step 3.6.1

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

$\frac{(2 m + 1) \sqrt{- m + 1}}{{({(- m + 1)}^{\frac{1}{2}})}^{2}}$

Step 3.6.2

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

$\frac{(2 m + 1) \sqrt{- m + 1}}{{(- m + 1)}^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

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

$\frac{(2 m + 1) \sqrt{- m + 1}}{{(- m + 1)}^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{(2 m + 1) \sqrt{- m + 1}}{{(- m + 1)}^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{(2 m + 1) \sqrt{- m + 1}}{{(- m + 1)}^{1}}$

Step 3.6.5

Simplify.

$\frac{(2 m + 1) \sqrt{- m + 1}}{- m + 1}$

Step 4

Factor $- 1$ out of $- m$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{- (m) + 1}$

Step 5

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{- (m) - 1 (- 1)}$

Step 6

Factor $- 1$ out of $- (m) - 1 (- 1)$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{- (m - 1)}$

Step 7

Rewrite negatives.

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Step 7.1

Rewrite $- (m - 1)$ as $- 1 (m - 1)$ .

$\frac{(2 m + 1) \sqrt{- m + 1}}{- 1 (m - 1)}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{(2 m + 1) \sqrt{- m + 1}}{m - 1}$

Step 7.3

Reorder factors in $- \frac{(2 m + 1) \sqrt{- m + 1}}{m - 1}$ .

$- \frac{\sqrt{- m + 1} (2 m + 1)}{m - 1}$