Algebra Examples

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

Step 1

To write $\frac{6 x}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 2

To write $- \frac{5}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

Step 3

Write each expression with a common denominator of $(x - 2) x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6 x}{x - 2}$ by $\frac{x}{x}$ .

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $(x - 2) x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1.1

Move $x$ .

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

Step 5.1.2

Multiply $x$ by $x$ .

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Multiply $- 5$ by $- 2$ .

$\frac{6 x^{2} - 5 x + 10}{x (x - 2)}$