Algebra Examples

$\frac{(2 x - 5) (2 x - 3)}{(4 x + 3) (2 x - 1)} \cdot \frac{4 x + 3}{4 x - 6}$

Step 1

Factor $2$ out of $4 x - 6$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$\frac{(2 x - 5) (2 x - 3)}{(4 x + 3) (2 x - 1)} \cdot \frac{4 x + 3}{2 (2 x) - 6}$

Step 1.2

Factor $2$ out of $- 6$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $2 x - 3$ .

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Step 2.1

Factor $2 x - 3$ out of $(2 x - 5) (2 x - 3)$ .

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

Step 2.2

Factor $2 x - 3$ out of $2 (2 x - 3)$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $4 x + 3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{2 x - 5}{2 x - 1} \cdot \frac{1}{2}$

Step 4

Multiply $\frac{2 x - 5}{2 x - 1}$ by $\frac{1}{2}$ .

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

Step 5

Move $2$ to the left of $2 x - 1$ .

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