Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write $4 x$ as a fraction with denominator $1$ .

$\frac{x}{5} + \frac{4 x}{1} + 3 (x - 5)$

Step 1.2

Multiply $\frac{4 x}{1}$ by $\frac{5}{5}$ .

$\frac{x}{5} + \frac{4 x}{1} \cdot \frac{5}{5} + 3 (x - 5)$

Step 1.3

Multiply $\frac{4 x}{1}$ by $\frac{5}{5}$ .

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

Step 1.4

Write $3 (x - 5)$ as a fraction with denominator $1$ .

$\frac{x}{5} + \frac{4 x \cdot 5}{5} + \frac{3 (x - 5)}{1}$

Step 1.5

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

$\frac{x}{5} + \frac{4 x \cdot 5}{5} + \frac{3 (x - 5)}{1} \cdot \frac{5}{5}$

Step 1.6

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $4$ .

$\frac{x + 20 x + 3 (x - 5) \cdot 5}{5}$

Step 3.2

Apply the distributive property.

$\frac{x + 20 x + (3 x + 3 \cdot - 5) \cdot 5}{5}$

Step 3.3

Multiply $3$ by $- 5$ .

$\frac{x + 20 x + (3 x - 15) \cdot 5}{5}$

Step 3.4

Apply the distributive property.

$\frac{x + 20 x + 3 x \cdot 5 - 15 \cdot 5}{5}$

Step 3.5

Multiply $5$ by $3$ .

$\frac{x + 20 x + 15 x - 15 \cdot 5}{5}$

Step 3.6

Multiply $- 15$ by $5$ .

$\frac{x + 20 x + 15 x - 75}{5}$

Step 4

Simplify terms.

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Step 4.1

Add $x$ and $20 x$ .

$\frac{21 x + 15 x - 75}{5}$

Step 4.2

Add $21 x$ and $15 x$ .

$\frac{36 x - 75}{5}$

Step 4.3

Factor $3$ out of $36 x - 75$ .

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Step 4.3.1

Factor $3$ out of $36 x$ .

$\frac{3 (12 x) - 75}{5}$

Step 4.3.2

Factor $3$ out of $- 75$ .

$\frac{3 (12 x) + 3 (- 25)}{5}$

Step 4.3.3

Factor $3$ out of $3 (12 x) + 3 (- 25)$ .

$\frac{3 (12 x - 25)}{5}$