Algebra Examples

$\frac{b x + 3 b}{x^{2} - 25} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 1

Factor $b$ out of $b x + 3 b$ .

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Step 1.1

Factor $b$ out of $b x$ .

$\frac{b (x) + 3 b}{x^{2} - 25} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 1.2

Factor $b$ out of $3 b$ .

$\frac{b (x) + b \cdot 3}{x^{2} - 25} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 1.3

Factor $b$ out of $b (x) + b \cdot 3$ .

$\frac{b (x + 3)}{x^{2} - 25} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{b (x + 3)}{x^{2} - 5^{2}} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{b (x + 3)}{(x + 5) (x - 5)} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$

Step 3

Simplify terms.

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Step 3.1

Factor $a$ out of $a x + 3 a$ .

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Step 3.1.1

Factor $a$ out of $a x$ .

$\frac{b (x + 3)}{(x + 5) (x - 5)} \cdot \frac{{(x - 5)}^{2}}{a (x) + 3 a}$

Step 3.1.2

Factor $a$ out of $3 a$ .

$\frac{b (x + 3)}{(x + 5) (x - 5)} \cdot \frac{{(x - 5)}^{2}}{a (x) + a \cdot 3}$

Step 3.1.3

Factor $a$ out of $a (x) + a \cdot 3$ .

$\frac{b (x + 3)}{(x + 5) (x - 5)} \cdot \frac{{(x - 5)}^{2}}{a (x + 3)}$

Step 3.2

Combine.

$\frac{b (x + 3) {(x - 5)}^{2}}{(x + 5) (x - 5) (a (x + 3))}$

Step 3.3

Cancel the common factor of $x + 3$ .

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Step 3.3.1

Cancel the common factor.

$\frac{b (x + 3) {(x - 5)}^{2}}{(x + 5) (x - 5) (a (x + 3))}$

Step 3.3.2

Rewrite the expression.

$\frac{b {(x - 5)}^{2}}{(x + 5) (x - 5) (a)}$

Step 3.4

Cancel the common factor of ${(x - 5)}^{2}$ and $x - 5$ .

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Step 3.4.1

Factor $x - 5$ out of $b {(x - 5)}^{2}$ .

$\frac{(x - 5) (b (x - 5))}{(x + 5) (x - 5) (a)}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $x - 5$ out of $(x + 5) (x - 5) (a)$ .

$\frac{(x - 5) (b (x - 5))}{(x - 5) ((x + 5) (a))}$

Step 3.4.2.2

Cancel the common factor.

$\frac{(x - 5) (b (x - 5))}{(x - 5) ((x + 5) (a))}$

Step 3.4.2.3

Rewrite the expression.

$\frac{b (x - 5)}{(x + 5) (a)}$

Step 3.5

Reorder factors in $\frac{b (x - 5)}{(x + 5) a}$ .

$\frac{b (x - 5)}{a (x + 5)}$