Algebra Examples

$\frac{3 x + 5}{35 x} + \frac{x - 3}{21 x}$

Step 1

To write $\frac{3 x + 5}{35 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x + 5}{35 x} \cdot \frac{3}{3} + \frac{x - 3}{21 x}$

Step 2

To write $\frac{x - 3}{21 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x + 5}{35 x} \cdot \frac{3}{3} + \frac{x - 3}{21 x} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $105 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 x + 5}{35 x}$ by $\frac{3}{3}$ .

$\frac{(3 x + 5) \cdot 3}{35 x \cdot 3} + \frac{x - 3}{21 x} \cdot \frac{5}{5}$

Step 3.2

Multiply $3$ by $35$ .

$\frac{(3 x + 5) \cdot 3}{105 x} + \frac{x - 3}{21 x} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{x - 3}{21 x}$ by $\frac{5}{5}$ .

$\frac{(3 x + 5) \cdot 3}{105 x} + \frac{(x - 3) \cdot 5}{21 x \cdot 5}$

Step 3.4

Multiply $5$ by $21$ .

$\frac{(3 x + 5) \cdot 3}{105 x} + \frac{(x - 3) \cdot 5}{105 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{(3 x + 5) \cdot 3 + (x - 3) \cdot 5}{105 x}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{3 x \cdot 3 + 5 \cdot 3 + (x - 3) \cdot 5}{105 x}$

Step 5.2

Multiply $3$ by $3$ .

$\frac{9 x + 5 \cdot 3 + (x - 3) \cdot 5}{105 x}$

Step 5.3

Multiply $5$ by $3$ .

$\frac{9 x + 15 + (x - 3) \cdot 5}{105 x}$

Step 5.4

Apply the distributive property.

$\frac{9 x + 15 + x \cdot 5 - 3 \cdot 5}{105 x}$

Step 5.5

Move $5$ to the left of $x$ .

$\frac{9 x + 15 + 5 \cdot x - 3 \cdot 5}{105 x}$

Step 5.6

Multiply $- 3$ by $5$ .

$\frac{9 x + 15 + 5 \cdot x - 15}{105 x}$

Step 5.7

Add $9 x$ and $5 x$ .

$\frac{14 x + 15 - 15}{105 x}$

Step 5.8

Subtract $15$ from $15$ .

$\frac{14 x + 0}{105 x}$

Step 5.9

Add $14 x$ and $0$ .

$\frac{14 x}{105 x}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $14$ and $105$ .

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Step 6.1.1

Factor $7$ out of $14 x$ .

$\frac{7 (2 x)}{105 x}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $7$ out of $105 x$ .

$\frac{7 (2 x)}{7 (15 x)}$

Step 6.1.2.2

Cancel the common factor.

$\frac{7 (2 x)}{7 (15 x)}$

Step 6.1.2.3

Rewrite the expression.

$\frac{2 x}{15 x}$

Step 6.2

Cancel the common factor of $x$ .

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Step 6.2.1

Cancel the common factor.

$\frac{2 x}{15 x}$

Step 6.2.2

Rewrite the expression.

$\frac{2}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{15}$

Decimal Form:

$0.1\overline{3}$