Finite Math Examples

$\frac{6}{m + 4} + \frac{6 m}{2 m - 3}$

Step 1

To write $\frac{6}{m + 4}$ as a fraction with a common denominator, multiply by $\frac{2 m - 3}{2 m - 3}$ .

$\frac{6}{m + 4} \cdot \frac{2 m - 3}{2 m - 3} + \frac{6 m}{2 m - 3}$

Step 2

To write $\frac{6 m}{2 m - 3}$ as a fraction with a common denominator, multiply by $\frac{m + 4}{m + 4}$ .

$\frac{6}{m + 4} \cdot \frac{2 m - 3}{2 m - 3} + \frac{6 m}{2 m - 3} \cdot \frac{m + 4}{m + 4}$

Step 3

Write each expression with a common denominator of $(m + 4) (2 m - 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{m + 4}$ by $\frac{2 m - 3}{2 m - 3}$ .

$\frac{6 (2 m - 3)}{(m + 4) (2 m - 3)} + \frac{6 m}{2 m - 3} \cdot \frac{m + 4}{m + 4}$

Step 3.2

Multiply $\frac{6 m}{2 m - 3}$ by $\frac{m + 4}{m + 4}$ .

$\frac{6 (2 m - 3)}{(m + 4) (2 m - 3)} + \frac{6 m (m + 4)}{(2 m - 3) (m + 4)}$

Step 3.3

Reorder the factors of $(m + 4) (2 m - 3)$ .

$\frac{6 (2 m - 3)}{(2 m - 3) (m + 4)} + \frac{6 m (m + 4)}{(2 m - 3) (m + 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (2 m - 3) + 6 m (m + 4)}{(2 m - 3) (m + 4)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $6$ out of $6 (2 m - 3) + 6 m (m + 4)$ .

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Step 5.1.1

Factor $6$ out of $6 m (m + 4)$ .

$\frac{6 (2 m - 3) + 6 (m (m + 4))}{(2 m - 3) (m + 4)}$

Step 5.1.2

Factor $6$ out of $6 (2 m - 3) + 6 (m (m + 4))$ .

$\frac{6 (2 m - 3 + m (m + 4))}{(2 m - 3) (m + 4)}$

Step 5.2

Apply the distributive property.

$\frac{6 (2 m - 3 + m \cdot m + m \cdot 4)}{(2 m - 3) (m + 4)}$

Step 5.3

Multiply $m$ by $m$ .

$\frac{6 (2 m - 3 + m^{2} + m \cdot 4)}{(2 m - 3) (m + 4)}$

Step 5.4

Move $4$ to the left of $m$ .

$\frac{6 (2 m - 3 + m^{2} + 4 \cdot m)}{(2 m - 3) (m + 4)}$

Step 5.5

Add $2 m$ and $4 m$ .

$\frac{6 (6 m - 3 + m^{2})}{(2 m - 3) (m + 4)}$

Step 5.6

Reorder terms.

$\frac{6 (m^{2} + 6 m - 3)}{(2 m - 3) (m + 4)}$