Simplify ((c^2-c-20)/(c^2-6c+5))÷((c^2-16)/(3c-3))

$\frac{c^{2} - c - 20}{c^{2} - 6 c + 5} \div \frac{c^{2} - 16}{3 c - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} - c - 20}{c^{2} - 6 c + 5} \cdot \frac{3 c - 3}{c^{2} - 16}$

Step 2

Factor $c^{2} - c - 20$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Write the factored form using these integers.

$\frac{(c - 5) (c + 4)}{c^{2} - 6 c + 5} \cdot \frac{3 c - 3}{c^{2} - 16}$

Step 3

Factor $c^{2} - 6 c + 5$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $5$ and whose sum is $- 6$ .

$- 5, - 1$

Write the factored form using these integers.

$\frac{(c - 5) (c + 4)}{(c - 5) (c - 1)} \cdot \frac{3 c - 3}{c^{2} - 16}$

Step 4

Simplify terms.

Cancel the common factor of $c - 5$ .

Cancel the common factor.

$\frac{(c - 5) (c + 4)}{(c - 5) (c - 1)} \cdot \frac{3 c - 3}{c^{2} - 16}$

Rewrite the expression.

$\frac{c + 4}{c - 1} \cdot \frac{3 c - 3}{c^{2} - 16}$

Factor $3$ out of $3 c - 3$ .

Factor $3$ out of $3 c$ .

$\frac{c + 4}{c - 1} \cdot \frac{3 (c) - 3}{c^{2} - 16}$

Factor $3$ out of $- 3$ .

$\frac{c + 4}{c - 1} \cdot \frac{3 (c) + 3 (- 1)}{c^{2} - 16}$

Factor $3$ out of $3 (c) + 3 (- 1)$ .

$\frac{c + 4}{c - 1} \cdot \frac{3 (c - 1)}{c^{2} - 16}$

Step 5

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{c + 4}{c - 1} \cdot \frac{3 (c - 1)}{c^{2} - 4^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 4$ .

$\frac{c + 4}{c - 1} \cdot \frac{3 (c - 1)}{(c + 4) (c - 4)}$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $c + 4$ .

Cancel the common factor.

$\frac{c + 4}{c - 1} \cdot \frac{3 (c - 1)}{(c + 4) (c - 4)}$

Rewrite the expression.

$\frac{1}{c - 1} \cdot \frac{3 (c - 1)}{c - 4}$

Cancel the common factor of $c - 1$ .

Factor $c - 1$ out of $3 (c - 1)$ .

$\frac{1}{c - 1} \cdot \frac{(c - 1) \cdot 3}{c - 4}$

Cancel the common factor.

$\frac{1}{c - 1} \cdot \frac{(c - 1) \cdot 3}{c - 4}$

Rewrite the expression.

$\frac{3}{c - 4}$

Simplify ((c^2-c-20)/(c^2-6c+5))÷((c^2-16)/(3c-3))

Related Questions

Support LCMGCF.com by disabling your adblocker.