Algebra Examples

$\frac{20 x - 4}{8 x^{2}} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 1

Factor $4$ out of $20 x - 4$ .

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Step 1.1

Factor $4$ out of $20 x$ .

$\frac{4 (5 x) - 4}{8 x^{2}} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{4 (5 x) + 4 (- 1)}{8 x^{2}} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 1.3

Factor $4$ out of $4 (5 x) + 4 (- 1)$ .

$\frac{4 (5 x - 1)}{8 x^{2}} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 2

Reduce the expression $\frac{4 (5 x - 1)}{8 x^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $4$ out of $8 x^{2}$ .

$\frac{4 (5 x - 1)}{4 (2 x^{2})} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 2.2

Cancel the common factor.

$\frac{4 (5 x - 1)}{4 (2 x^{2})} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 2.3

Rewrite the expression.

$\frac{5 x - 1}{2 x^{2}} \div (5 x - 1) \cdot \frac{6 x}{5}$

Step 3

Rewrite the division as a fraction.

$\frac{\frac{5 x - 1}{2 x^{2}}}{5 x - 1} \cdot \frac{6 x}{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 x - 1}{2 x^{2}} \cdot \frac{1}{5 x - 1} \cdot \frac{6 x}{5}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $5 x - 1$ .

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Step 5.1.1

Cancel the common factor.

$\frac{5 x - 1}{2 x^{2}} \cdot \frac{1}{5 x - 1} \cdot \frac{6 x}{5}$

Step 5.1.2

Rewrite the expression.

$\frac{1}{2 x^{2}} \cdot \frac{6 x}{5}$

Step 5.2

Combine.

$\frac{1 (6 x)}{2 x^{2} \cdot 5}$

Step 5.3

Cancel the common factor of $6$ and $2$ .

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Step 5.3.1

Factor $2$ out of $1 (6 x)$ .

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

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $2$ out of $2 x^{2} \cdot 5$ .

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

Step 5.3.2.2

Cancel the common factor.

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

Step 5.3.2.3

Rewrite the expression.

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

Step 5.4

Cancel the common factor of $x$ and $x^{2}$ .

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Step 5.4.1

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

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

Step 5.4.2

Cancel the common factors.

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Step 5.4.2.1

Factor $x$ out of $x^{2} \cdot 5$ .

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

Step 5.4.2.2

Cancel the common factor.

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

Step 5.4.2.3

Rewrite the expression.

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

Step 6

Multiply $3$ by $1$ .

$\frac{3}{x \cdot 5}$

Step 7

Move $5$ to the left of $x$ .

$\frac{3}{5 x}$