Divide ((a^2-6a+5)/(a^2-15a+56))÷((a^2+2a-35)/(a^2-5a-24))

$\frac{a^{2} - 6 a + 5}{a^{2} - 15 a + 56} \div \frac{a^{2} + 2 a - 35}{a^{2} - 5 a - 24}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2} - 6 a + 5}{a^{2} - 15 a + 56} \cdot \frac{a^{2} - 5 a - 24}{a^{2} + 2 a - 35}$

Step 2

Factor $a^{2} - 6 a + 5$ 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.

$\frac{(a - 5) (a - 1)}{a^{2} - 15 a + 56} \cdot \frac{a^{2} - 5 a - 24}{a^{2} + 2 a - 35}$

Step 3

Factor $a^{2} - 15 a + 56$ 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 $56$ and whose sum is $- 15$ .

$- 8, - 7$

Write the factored form using these integers.

$\frac{(a - 5) (a - 1)}{(a - 8) (a - 7)} \cdot \frac{a^{2} - 5 a - 24}{a^{2} + 2 a - 35}$

Step 4

Factor $a^{2} - 5 a - 24$ 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 $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$\frac{(a - 5) (a - 1)}{(a - 8) (a - 7)} \cdot \frac{(a - 8) (a + 3)}{a^{2} + 2 a - 35}$

Step 5

Factor $a^{2} + 2 a - 35$ 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 $- 35$ and whose sum is $2$ .

$- 5, 7$

Write the factored form using these integers.

$\frac{(a - 5) (a - 1)}{(a - 8) (a - 7)} \cdot \frac{(a - 8) (a + 3)}{(a - 5) (a + 7)}$

Step 6

Cancel the common factor of $a - 5$ .

Cancel the common factor.

$\frac{(a - 5) (a - 1)}{(a - 8) (a - 7)} \cdot \frac{(a - 8) (a + 3)}{(a - 5) (a + 7)}$

Rewrite the expression.

$\frac{a - 1}{(a - 8) (a - 7)} \cdot \frac{(a - 8) (a + 3)}{a + 7}$

Step 7

Cancel the common factor of $a - 8$ .

Cancel the common factor.

$\frac{a - 1}{(a - 8) (a - 7)} \cdot \frac{(a - 8) (a + 3)}{a + 7}$

Rewrite the expression.

$\frac{a - 1}{a - 7} \cdot \frac{a + 3}{a + 7}$

Step 8

Multiply $\frac{a - 1}{a - 7}$ by $\frac{a + 3}{a + 7}$ .

$\frac{(a - 1) (a + 3)}{(a - 7) (a + 7)}$

Divide ((a^2-6a+5)/(a^2-15a+56))÷((a^2+2a-35)/(a^2-5a-24))

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