Basic Math Examples

\frac{c - 4}{c + 4} \div \frac{4 - c}{16 + c^{2}}

$\frac{c - 4}{c + 4} \div \frac{4 - c}{16 + c^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

\frac{c - 4}{c + 4} \cdot \frac{16 + c^{2}}{4 - c}

$\frac{c - 4}{c + 4} \cdot \frac{16 + c^{2}}{4 - c}$

Step 2

Multiply

\frac{c - 4}{c + 4}

$\frac{c - 4}{c + 4}$ by

\frac{16 + c^{2}}{4 - c}

$\frac{16 + c^{2}}{4 - c}$ .

\frac{(c - 4) (16 + c^{2})}{(c + 4) (4 - c)}

$\frac{(c - 4) (16 + c^{2})}{(c + 4) (4 - c)}$

Step 3

Cancel the common factor of

c - 4

$c - 4$ and

4 - c

$4 - c$ .

Tap for more steps...

Step 3.1

Factor

- 1

$- 1$ out of

c

$c$ .

\frac{(- 1 (- c) - 4) (16 + c^{2})}{(c + 4) (4 - c)}

$\frac{(- 1 (- c) - 4) (16 + c^{2})}{(c + 4) (4 - c)}$

Step 3.2

Rewrite

- 4

$- 4$ as

- 1 (4)

$- 1 (4)$ .

\frac{(- 1 (- c) - 1 (4)) (16 + c^{2})}{(c + 4) (4 - c)}

$\frac{(- 1 (- c) - 1 (4)) (16 + c^{2})}{(c + 4) (4 - c)}$

Step 3.3

Factor

- 1

$- 1$ out of

- 1 (- c) - 1 (4)

$- 1 (- c) - 1 (4)$ .

\frac{- 1 (- c + 4) (16 + c^{2})}{(c + 4) (4 - c)}

$\frac{- 1 (- c + 4) (16 + c^{2})}{(c + 4) (4 - c)}$

Step 3.4

Reorder terms.

\frac{- 1 (- c + 4) (16 + c^{2})}{(c + 4) (- c + 4)}

$\frac{- 1 (- c + 4) (16 + c^{2})}{(c + 4) (- c + 4)}$

Step 3.5

Cancel the common factor.

$\frac{- 1 (- c + 4) (16 + c^{2})}{(c + 4) (- c + 4)}$

Step 3.6

Rewrite the expression.

$\frac{- 1 (16 + c^{2})}{c + 4}$

Step 4

Move the negative in front of the fraction.

$- \frac{16 + c^{2}}{c + 4}$