Algebra Examples

$\frac{7 a^{2}}{7 a^{3} + 56 a^{2}} \div \frac{2}{a^{2} + 7 a - 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 a^{2}}{7 a^{3} + 56 a^{2}} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2

Simplify terms.

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Step 2.1

Factor $7 a^{2}$ out of $7 a^{3} + 56 a^{2}$ .

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Step 2.1.1

Factor $7 a^{2}$ out of $7 a^{3}$ .

$\frac{7 a^{2}}{7 a^{2} (a) + 56 a^{2}} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.1.2

Factor $7 a^{2}$ out of $56 a^{2}$ .

$\frac{7 a^{2}}{7 a^{2} (a) + 7 a^{2} (8)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.1.3

Factor $7 a^{2}$ out of $7 a^{2} (a) + 7 a^{2} (8)$ .

$\frac{7 a^{2}}{7 a^{2} (a + 8)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.2

Cancel the common factor of $7$ .

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Step 2.2.1

Cancel the common factor.

$\frac{7 a^{2}}{7 a^{2} (a + 8)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.2.2

Rewrite the expression.

$\frac{a^{2}}{a^{2} (a + 8)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.3

Cancel the common factor of $a^{2}$ .

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Step 2.3.1

Cancel the common factor.

$\frac{a^{2}}{a^{2} (a + 8)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{a + 8} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 3

Factor $a^{2} + 7 a - 8$ using the AC method.

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Step 3.1

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 $- 8$ and whose sum is $7$ .

$- 1, 8$

Step 3.2

Write the factored form using these integers.

$\frac{1}{a + 8} \cdot \frac{(a - 1) (a + 8)}{2}$

Step 4

Cancel the common factor of $a + 8$ .

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Step 4.1

Factor $a + 8$ out of $(a - 1) (a + 8)$ .

$\frac{1}{a + 8} \cdot \frac{(a + 8) (a - 1)}{2}$

Step 4.2

Cancel the common factor.

$\frac{1}{a + 8} \cdot \frac{(a + 8) (a - 1)}{2}$

Step 4.3

Rewrite the expression.

$\frac{a - 1}{2}$