Algebra Examples

$\frac{2 x (x - 1)}{5 (x + 3)} \cdot \frac{15 (x + 3)}{4 x}$

Step 1

Cancel the common factor of $2 x$ .

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Step 1.1

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

$\frac{2 x (x - 1)}{5 (x + 3)} \cdot \frac{15 (x + 3)}{2 x (2)}$

Step 1.2

Cancel the common factor.

$\frac{2 x (x - 1)}{5 (x + 3)} \cdot \frac{15 (x + 3)}{2 x \cdot 2}$

Step 1.3

Rewrite the expression.

$\frac{x - 1}{5 (x + 3)} \cdot \frac{15 (x + 3)}{2}$

Step 2

Cancel the common factor of $5 (x + 3)$ .

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Step 2.1

Factor $5 (x + 3)$ out of $15 (x + 3)$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Apply the distributive property.

$x \frac{3}{2} - 1 (\frac{3}{2})$

Step 4

Combine $x$ and $\frac{3}{2}$ .

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

Step 5

Rewrite $- 1 (\frac{3}{2})$ as $- (\frac{3}{2})$ .

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

Step 6

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - 3}{2}$

Step 7

Reorder factors in $x \cdot 3 - 3$ .

$\frac{3 x - 3}{2}$

Step 8

Factor $3$ out of $3 x - 3$ .

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Step 8.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 3}{2}$

Step 8.2

Factor $3$ out of $- 3$ .

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

Step 8.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\frac{3 (x - 1)}{2}$