Algebra Examples

$\frac{a^{2}}{5 (a - b)} - \frac{b^{2}}{4 (a - b)}$

Step 1

To write $\frac{a^{2}}{5 (a - b)}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{a^{2}}{5 (a - b)} \cdot \frac{4}{4} - \frac{b^{2}}{4 (a - b)}$

Step 2

To write $- \frac{b^{2}}{4 (a - b)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{a^{2}}{5 (a - b)} \cdot \frac{4}{4} - \frac{b^{2}}{4 (a - b)} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $20 (a - b)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{a^{2}}{5 (a - b)}$ by $\frac{4}{4}$ .

$\frac{a^{2} \cdot 4}{5 (a - b) \cdot 4} - \frac{b^{2}}{4 (a - b)} \cdot \frac{5}{5}$

Step 3.2

Multiply $4$ by $5$ .

$\frac{a^{2} \cdot 4}{20 (a - b)} - \frac{b^{2}}{4 (a - b)} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{b^{2}}{4 (a - b)}$ by $\frac{5}{5}$ .

$\frac{a^{2} \cdot 4}{20 (a - b)} - \frac{b^{2} \cdot 5}{4 (a - b) \cdot 5}$

Step 3.4

Multiply $5$ by $4$ .

$\frac{a^{2} \cdot 4}{20 (a - b)} - \frac{b^{2} \cdot 5}{20 (a - b)}$

Step 4

Combine the numerators over the common denominator.

$\frac{a^{2} \cdot 4 - b^{2} \cdot 5}{20 (a - b)}$

Step 5

Simplify the numerator.

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Step 5.1

Move $4$ to the left of $a^{2}$ .

$\frac{4 \cdot a^{2} - b^{2} \cdot 5}{20 (a - b)}$

Step 5.2

Multiply $5$ by $- 1$ .

$\frac{4 a^{2} - 5 b^{2}}{20 (a - b)}$