Pre-Algebra Examples

$2 + \frac{26}{2 x - 10} \cdot x - 5$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 x - 10$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

$2 + \frac{26}{2 (x) - 10} \cdot x - 5$

Step 1.1.2

Factor $2$ out of $- 10$ .

$2 + \frac{26}{2 x + 2 \cdot - 5} \cdot x - 5$

Step 1.1.3

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$2 + \frac{26}{2 (x - 5)} \cdot x - 5$

Step 1.2

Cancel the common factor of $26$ and $2$ .

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Step 1.2.1

Factor $2$ out of $26$ .

$2 + \frac{2 \cdot 13}{2 (x - 5)} \cdot x - 5$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Cancel the common factor.

$2 + \frac{2 \cdot 13}{2 (x - 5)} \cdot x - 5$

Step 1.2.2.2

Rewrite the expression.

$2 + \frac{13}{x - 5} \cdot x - 5$

Step 1.3

Combine $\frac{13}{x - 5}$ and $x$ .

$2 + \frac{13 x}{x - 5} - 5$

Step 2

Find the common denominator.

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Step 2.1

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} + \frac{13 x}{x - 5} - 5$

Step 2.2

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

$\frac{2}{1} \cdot \frac{x - 5}{x - 5} + \frac{13 x}{x - 5} - 5$

Step 2.3

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

$\frac{2 (x - 5)}{x - 5} + \frac{13 x}{x - 5} - 5$

Step 2.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{2 (x - 5)}{x - 5} + \frac{13 x}{x - 5} + \frac{- 5}{1}$

Step 2.5

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

$\frac{2 (x - 5)}{x - 5} + \frac{13 x}{x - 5} + \frac{- 5}{1} \cdot \frac{x - 5}{x - 5}$

Step 2.6

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

$\frac{2 (x - 5)}{x - 5} + \frac{13 x}{x - 5} + \frac{- 5 (x - 5)}{x - 5}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 (x - 5) + 13 x - 5 (x - 5)}{x - 5}$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$\frac{2 x + 2 \cdot - 5 + 13 x - 5 (x - 5)}{x - 5}$

Step 4.2

Multiply $2$ by $- 5$ .

$\frac{2 x - 10 + 13 x - 5 (x - 5)}{x - 5}$

Step 4.3

Apply the distributive property.

$\frac{2 x - 10 + 13 x - 5 x - 5 \cdot - 5}{x - 5}$

Step 4.4

Multiply $- 5$ by $- 5$ .

$\frac{2 x - 10 + 13 x - 5 x + 25}{x - 5}$

Step 5

Simplify terms.

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Step 5.1

Add $2 x$ and $13 x$ .

$\frac{15 x - 10 - 5 x + 25}{x - 5}$

Step 5.2

Subtract $5 x$ from $15 x$ .

$\frac{10 x - 10 + 25}{x - 5}$

Step 5.3

Add $- 10$ and $25$ .

$\frac{10 x + 15}{x - 5}$

Step 5.4

Factor $5$ out of $10 x + 15$ .

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Step 5.4.1

Factor $5$ out of $10 x$ .

$\frac{5 (2 x) + 15}{x - 5}$

Step 5.4.2

Factor $5$ out of $15$ .

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

Step 5.4.3

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

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