Algebra Examples

$\frac{5 x - 20}{4 x^{2} - 25} \cdot \frac{2 x - 5}{5 x + 3}$

Step 1

Factor $5$ out of $5 x - 20$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 20}{4 x^{2} - 25} \cdot \frac{2 x - 5}{5 x + 3}$

Step 1.2

Factor $5$ out of $- 20$ .

$\frac{5 x + 5 \cdot - 4}{4 x^{2} - 25} \cdot \frac{2 x - 5}{5 x + 3}$

Step 1.3

Factor $5$ out of $5 x + 5 \cdot - 4$ .

$\frac{5 (x - 4)}{4 x^{2} - 25} \cdot \frac{2 x - 5}{5 x + 3}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\frac{5 (x - 4)}{{(2 x)}^{2} - 25} \cdot \frac{2 x - 5}{5 x + 3}$

Step 2.2

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

$\frac{5 (x - 4)}{{(2 x)}^{2} - 5^{2}} \cdot \frac{2 x - 5}{5 x + 3}$

Step 2.3

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

$\frac{5 (x - 4)}{(2 x + 5) (2 x - 5)} \cdot \frac{2 x - 5}{5 x + 3}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $2 x - 5$ .

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Step 3.1.1

Factor $2 x - 5$ out of $(2 x + 5) (2 x - 5)$ .

$\frac{5 (x - 4)}{(2 x - 5) (2 x + 5)} \cdot \frac{2 x - 5}{5 x + 3}$

Step 3.1.2

Cancel the common factor.

$\frac{5 (x - 4)}{(2 x - 5) (2 x + 5)} \cdot \frac{2 x - 5}{5 x + 3}$

Step 3.1.3

Rewrite the expression.

$\frac{5 (x - 4)}{2 x + 5} \cdot \frac{1}{5 x + 3}$

Step 3.2

Multiply $\frac{5 (x - 4)}{2 x + 5}$ by $\frac{1}{5 x + 3}$ .

$\frac{5 (x - 4)}{(2 x + 5) (5 x + 3)}$