Finite Math Examples

$\frac{- 9}{m n^{2}} + \frac{m^{2}}{n}$

Step 1

Move the negative in front of the fraction.

$- \frac{9}{m n^{2}} + \frac{m^{2}}{n}$

Step 2

To write $\frac{m^{2}}{n}$ as a fraction with a common denominator, multiply by $\frac{m n}{m n}$ .

$- \frac{9}{m n^{2}} + \frac{m^{2}}{n} \cdot \frac{m n}{m n}$

Step 3

Write each expression with a common denominator of $m n^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{m^{2}}{n}$ by $\frac{m n}{m n}$ .

$- \frac{9}{m n^{2}} + \frac{m^{2} (m n)}{n (m n)}$

Step 3.2

Raise $n$ to the power of $1$ .

$- \frac{9}{m n^{2}} + \frac{m^{2} (m n)}{m (n^{1} n)}$

Step 3.3

Raise $n$ to the power of $1$ .

$- \frac{9}{m n^{2}} + \frac{m^{2} (m n)}{m (n^{1} n^{1})}$

Step 3.4

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

$- \frac{9}{m n^{2}} + \frac{m^{2} (m n)}{m n^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$- \frac{9}{m n^{2}} + \frac{m^{2} (m n)}{m n^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 9 + m^{2} (m n)}{m n^{2}}$

Step 5

Multiply $m^{2}$ by $m$ by adding the exponents.

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Step 5.1

Move $m$ .

$\frac{- 9 + m \cdot m^{2} n}{m n^{2}}$

Step 5.2

Multiply $m$ by $m^{2}$ .

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Step 5.2.1

Raise $m$ to the power of $1$ .

$\frac{- 9 + m^{1} m^{2} n}{m n^{2}}$

Step 5.2.2

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

$\frac{- 9 + m^{1 + 2} n}{m n^{2}}$

Step 5.3

Add $1$ and $2$ .

$\frac{- 9 + m^{3} n}{m n^{2}}$

Step 6

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 (9) + m^{3} n}{m n^{2}}$

Step 7

Factor $- 1$ out of $m^{3} n$ .

$\frac{- 1 (9) - (- m^{3} n)}{m n^{2}}$

Step 8

Factor $- 1$ out of $- 1 (9) - (- m^{3} n)$ .

$\frac{- 1 (9 - m^{3} n)}{m n^{2}}$

Step 9

Move the negative in front of the fraction.

$- \frac{9 - m^{3} n}{m n^{2}}$