Basic Math Examples

$\frac{4}{m - 2} - \frac{3}{m + 4} + 5$

Step 1

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

$\frac{4}{m - 2} \cdot \frac{m + 4}{m + 4} - \frac{3}{m + 4} + 5$

Step 2

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

$\frac{4}{m - 2} \cdot \frac{m + 4}{m + 4} - \frac{3}{m + 4} \cdot \frac{m - 2}{m - 2} + 5$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{4 (m + 4)}{(m - 2) (m + 4)} - \frac{3}{m + 4} \cdot \frac{m - 2}{m - 2} + 5$

Step 3.2

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

$\frac{4 (m + 4)}{(m - 2) (m + 4)} - \frac{3 (m - 2)}{(m + 4) (m - 2)} + 5$

Step 3.3

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

$\frac{4 (m + 4)}{(m + 4) (m - 2)} - \frac{3 (m - 2)}{(m + 4) (m - 2)} + 5$

Step 4

Combine the numerators over the common denominator.

$\frac{4 (m + 4) - 3 (m - 2)}{(m + 4) (m - 2)} + 5$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{4 m + 4 \cdot 4 - 3 (m - 2)}{(m + 4) (m - 2)} + 5$

Step 5.2

Multiply $4$ by $4$ .

$\frac{4 m + 16 - 3 (m - 2)}{(m + 4) (m - 2)} + 5$

Step 5.3

Apply the distributive property.

$\frac{4 m + 16 - 3 m - 3 \cdot - 2}{(m + 4) (m - 2)} + 5$

Step 5.4

Multiply $- 3$ by $- 2$ .

$\frac{4 m + 16 - 3 m + 6}{(m + 4) (m - 2)} + 5$

Step 5.5

Subtract $3 m$ from $4 m$ .

$\frac{m + 16 + 6}{(m + 4) (m - 2)} + 5$

Step 5.6

Add $16$ and $6$ .

$\frac{m + 22}{(m + 4) (m - 2)} + 5$

Step 6

To write $5$ as a fraction with a common denominator, multiply by $\frac{(m + 4) (m - 2)}{(m + 4) (m - 2)}$ .

$\frac{m + 22}{(m + 4) (m - 2)} + 5 \cdot \frac{(m + 4) (m - 2)}{(m + 4) (m - 2)}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Combine $5$ and $\frac{(m + 4) (m - 2)}{(m + 4) (m - 2)}$ .

$\frac{m + 22}{(m + 4) (m - 2)} + \frac{5 ((m + 4) (m - 2))}{(m + 4) (m - 2)}$

Step 7.2

Combine the numerators over the common denominator.

$\frac{m + 22 + 5 ((m + 4) (m - 2))}{(m + 4) (m - 2)}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Apply the distributive property.

$\frac{m + 22 + (5 m + 5 \cdot 4) (m - 2)}{(m + 4) (m - 2)}$

Step 8.2

Multiply $5$ by $4$ .

$\frac{m + 22 + (5 m + 20) (m - 2)}{(m + 4) (m - 2)}$

Step 8.3

Expand $(5 m + 20) (m - 2)$ using the FOIL Method.

Tap for more steps...

Step 8.3.1

Apply the distributive property.

$\frac{m + 22 + 5 m (m - 2) + 20 (m - 2)}{(m + 4) (m - 2)}$

Step 8.3.2

Apply the distributive property.

$\frac{m + 22 + 5 m \cdot m + 5 m \cdot - 2 + 20 (m - 2)}{(m + 4) (m - 2)}$

Step 8.3.3

Apply the distributive property.

$\frac{m + 22 + 5 m \cdot m + 5 m \cdot - 2 + 20 m + 20 \cdot - 2}{(m + 4) (m - 2)}$

Step 8.4

Simplify and combine like terms.

Tap for more steps...

Step 8.4.1

Simplify each term.

Tap for more steps...

Step 8.4.1.1

Multiply $m$ by $m$ by adding the exponents.

Tap for more steps...

Step 8.4.1.1.1

Move $m$ .

$\frac{m + 22 + 5 (m \cdot m) + 5 m \cdot - 2 + 20 m + 20 \cdot - 2}{(m + 4) (m - 2)}$

Step 8.4.1.1.2

Multiply $m$ by $m$ .

$\frac{m + 22 + 5 m^{2} + 5 m \cdot - 2 + 20 m + 20 \cdot - 2}{(m + 4) (m - 2)}$

Step 8.4.1.2

Multiply $- 2$ by $5$ .

$\frac{m + 22 + 5 m^{2} - 10 m + 20 m + 20 \cdot - 2}{(m + 4) (m - 2)}$

Step 8.4.1.3

Multiply $20$ by $- 2$ .

$\frac{m + 22 + 5 m^{2} - 10 m + 20 m - 40}{(m + 4) (m - 2)}$

Step 8.4.2

Add $- 10 m$ and $20 m$ .

$\frac{m + 22 + 5 m^{2} + 10 m - 40}{(m + 4) (m - 2)}$

Step 8.5

Add $m$ and $10 m$ .

$\frac{11 m + 22 + 5 m^{2} - 40}{(m + 4) (m - 2)}$

Step 8.6

Subtract $40$ from $22$ .

$\frac{11 m + 5 m^{2} - 18}{(m + 4) (m - 2)}$

Step 8.7

Reorder terms.

$\frac{5 m^{2} + 11 m - 18}{(m + 4) (m - 2)}$