Algebra Examples

$\frac{3}{x^{2} + 14 x + 48} \div \frac{3}{10 x + 60}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{x^{2} + 14 x + 48} \cdot \frac{10 x + 60}{3}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3}{x^{2} + 14 x + 48} \cdot \frac{10 x + 60}{3}$

Step 2.2

Rewrite the expression.

$\frac{1}{x^{2} + 14 x + 48} (10 x + 60)$

Step 3

Factor $x^{2} + 14 x + 48$ 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 $48$ and whose sum is $14$ .

$6, 8$

Step 3.2

Write the factored form using these integers.

$\frac{1}{(x + 6) (x + 8)} (10 x + 60)$

Step 4

Simplify terms.

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Step 4.1

Multiply $\frac{1}{(x + 6) (x + 8)}$ by $10 x + 60$ .

$\frac{10 x + 60}{(x + 6) (x + 8)}$

Step 4.2

Factor $10$ out of $10 x + 60$ .

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Step 4.2.1

Factor $10$ out of $10 x$ .

$\frac{10 (x) + 60}{(x + 6) (x + 8)}$

Step 4.2.2

Factor $10$ out of $60$ .

$\frac{10 x + 10 \cdot 6}{(x + 6) (x + 8)}$

Step 4.2.3

Factor $10$ out of $10 x + 10 \cdot 6$ .

$\frac{10 (x + 6)}{(x + 6) (x + 8)}$

Step 4.3

Cancel the common factor of $x + 6$ .

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Step 4.3.1

Cancel the common factor.

$\frac{10 (x + 6)}{(x + 6) (x + 8)}$

Step 4.3.2

Rewrite the expression.

$\frac{10}{x + 8}$