Algebra Examples

$\frac{3 x}{5} - \frac{2 x}{9}$

Step 1

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{3 x}{5} \cdot \frac{9}{9} - \frac{2 x}{9}$

Step 2

To write $- \frac{2 x}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5} \cdot \frac{9}{9} - \frac{2 x}{9} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 x}{5}$ by $\frac{9}{9}$ .

$\frac{3 x \cdot 9}{5 \cdot 9} - \frac{2 x}{9} \cdot \frac{5}{5}$

Step 3.2

Multiply $5$ by $9$ .

$\frac{3 x \cdot 9}{45} - \frac{2 x}{9} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{2 x}{9}$ by $\frac{5}{5}$ .

$\frac{3 x \cdot 9}{45} - \frac{2 x \cdot 5}{9 \cdot 5}$

Step 3.4

Multiply $9$ by $5$ .

$\frac{3 x \cdot 9}{45} - \frac{2 x \cdot 5}{45}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 9 - 2 x \cdot 5}{45}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $x$ out of $3 x \cdot 9 - 2 x \cdot 5$ .

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Step 5.1.1

Factor $x$ out of $3 x \cdot 9$ .

$\frac{x (3 \cdot 9) - 2 x \cdot 5}{45}$

Step 5.1.2

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

$\frac{x (3 \cdot 9) + x (- 2 \cdot 5)}{45}$

Step 5.1.3

Factor $x$ out of $x (3 \cdot 9) + x (- 2 \cdot 5)$ .

$\frac{x (3 \cdot 9 - 2 \cdot 5)}{45}$

Step 5.2

Multiply $3$ by $9$ .

$\frac{x (27 - 2 \cdot 5)}{45}$

Step 5.3

Multiply $- 2$ by $5$ .

$\frac{x (27 - 10)}{45}$

Step 5.4

Subtract $10$ from $27$ .

$\frac{x \cdot 17}{45}$

Step 6

Move $17$ to the left of $x$ .

$\frac{17 x}{45}$