Algebra Examples

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

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

Step 1

Find the common denominator.

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Step 1.1

Write

4 x

$4 x$ as a fraction with denominator

1

$1$ .

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

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

Step 1.2

Multiply

\frac{4 x}{1}

$\frac{4 x}{1}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.3

Multiply

\frac{4 x}{1}

$\frac{4 x}{1}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.4

Write

3 (x - 5)

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

1

$1$ .

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

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

Step 1.5

Multiply

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

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

\frac{5}{5}

$\frac{5}{5}$ .

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

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

\frac{5}{5}

$\frac{5}{5}$ .

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

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

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply

5

$5$ by

4

$4$ .

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

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

Step 3.2

Apply the distributive property.

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

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

Step 3.3

Multiply

3

$3$ by

- 5

$- 5$ .

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

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

Step 3.5

Multiply

5

$5$ by

3

$3$ .

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

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

Step 3.6

Multiply

- 15

$- 15$ by

5

$5$ .

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

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

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

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

Step 4

Simplify terms.

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Step 4.1

Add

x

$x$ and

20 x

$20 x$ .

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

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

Step 4.2

Add

21 x

$21 x$ and

15 x

$15 x$ .

\frac{36 x - 75}{5}

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

Step 4.3

Factor

3

$3$ out of

36 x - 75

$36 x - 75$ .

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Step 4.3.1

Factor

3

$3$ out of

36 x

$36 x$ .

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

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

Step 4.3.2

Factor

3

$3$ out of

- 75

$- 75$ .

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

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

Step 4.3.3

Factor

3

$3$ out of

3 (12 x) + 3 (- 25)

$3 (12 x) + 3 (- 25)$ .

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

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

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

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

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

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