Algebra Examples

$\frac{2 x + 10}{4 x} \div \frac{x^{2} + 8 x + 15}{6 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x + 10}{4 x} \cdot \frac{6 x^{2}}{x^{2} + 8 x + 15}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2 x$ .

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Step 2.1.1

Factor $2 x$ out of $4 x$ .

$\frac{2 x + 10}{2 x (2)} \cdot \frac{6 x^{2}}{x^{2} + 8 x + 15}$

Step 2.1.2

Factor $2 x$ out of $6 x^{2}$ .

$\frac{2 x + 10}{2 x (2)} \cdot \frac{2 x (3 x)}{x^{2} + 8 x + 15}$

Step 2.1.3

Cancel the common factor.

$\frac{2 x + 10}{2 x \cdot 2} \cdot \frac{2 x (3 x)}{x^{2} + 8 x + 15}$

Step 2.1.4

Rewrite the expression.

$\frac{2 x + 10}{2} \cdot \frac{3 x}{x^{2} + 8 x + 15}$

Step 2.2

Multiply $\frac{2 x + 10}{2}$ by $\frac{3 x}{x^{2} + 8 x + 15}$ .

$\frac{(2 x + 10) (3 x)}{2 (x^{2} + 8 x + 15)}$

Step 2.3

Cancel the common factor of $2 x + 10$ and $2$ .

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Step 2.3.1

Factor $2$ out of $(2 x + 10) (3 x)$ .

$\frac{2 ((x + 5) (3 x))}{2 (x^{2} + 8 x + 15)}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Cancel the common factor.

$\frac{2 ((x + 5) (3 x))}{2 (x^{2} + 8 x + 15)}$

Step 2.3.2.2

Rewrite the expression.

$\frac{(x + 5) (3 x)}{x^{2} + 8 x + 15}$

Step 3

Factor $x^{2} + 8 x + 15$ 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 $15$ and whose sum is $8$ .

$3, 5$

Step 3.2

Write the factored form using these integers.

$\frac{(x + 5) \cdot 3 x}{(x + 3) (x + 5)}$

Step 4

Cancel the common factor of $x + 5$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 5) \cdot 3 x}{(x + 3) (x + 5)}$

Step 4.2

Rewrite the expression.

$\frac{3 x}{x + 3}$