Algebra Examples

$\frac{\frac{6 x - 3}{x^{2}}}{\frac{5}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 x - 3}{x^{2}} \cdot \frac{x}{5}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

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

$\frac{6 x - 3}{x \cdot x} \cdot \frac{x}{5}$

Step 2.2

Cancel the common factor.

$\frac{6 x - 3}{x \cdot x} \cdot \frac{x}{5}$

Step 2.3

Rewrite the expression.

$\frac{6 x - 3}{x} \cdot \frac{1}{5}$

$\frac{6 x - 3}{x} \cdot \frac{1}{5}$

Step 3

Multiply $\frac{6 x - 3}{x}$ by $\frac{1}{5}$ .

$\frac{6 x - 3}{x \cdot 5}$

Step 4

Factor $3$ out of $6 x - 3$ .

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Step 4.1

Factor $3$ out of $6 x$ .

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

Step 4.2

Factor $3$ out of $- 3$ .

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

Step 4.3

Factor $3$ out of $3 (2 x) + 3 (- 1)$ .

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

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot - 1}{5 x}$

Step 8

Multiply $3$ by $- 1$ .

$\frac{6 x - 3}{5 x}$

Step 9

Split the fraction $\frac{6 x - 3}{5 x}$ into two fractions.

$\frac{6 x}{5 x} + \frac{- 3}{5 x}$

Step 10

Cancel the common factor of $x$ .

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Step 10.1

Cancel the common factor.

$\frac{6 x}{5 x} + \frac{- 3}{5 x}$

Step 10.2

Rewrite the expression.

$\frac{6}{5} + \frac{- 3}{5 x}$

$\frac{6}{5} + \frac{- 3}{5 x}$

Step 11

Move the negative in front of the fraction.

$\frac{6}{5} - \frac{3}{5 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$