Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Factor $2 x$ out of $2 x^{2} - 6 x$ .

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Cancel the common factor of $x$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 1.3

Factor $x$ out of $x^{2} - 3 x$ .

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.3.3

Factor $x$ out of $x \cdot x + x \cdot - 3$ .

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

Step 1.4

Cancel the common factor of $x$ .

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Step 1.4.1

Cancel the common factor.

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

Step 1.4.2

Rewrite the expression.

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

Step 2

To write $- \frac{2}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $2 (x - 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{x - 3}$ by $\frac{2}{2}$ .

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

Step 3.2

Reorder the factors of $(x - 3) \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $2$ .

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

Step 5.2

Subtract $4$ from $5$ .

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