Basic Math Examples

$\frac{a^{2}}{a - 3} - \frac{4}{5 a - 15}$

Step 1

Factor $5$ out of $5 a - 15$ .

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Step 1.1

Factor $5$ out of $5 a$ .

$\frac{a^{2}}{a - 3} - \frac{4}{5 (a) - 15}$

Step 1.2

Factor $5$ out of $- 15$ .

$\frac{a^{2}}{a - 3} - \frac{4}{5 a + 5 \cdot - 3}$

Step 1.3

Factor $5$ out of $5 a + 5 \cdot - 3$ .

$\frac{a^{2}}{a - 3} - \frac{4}{5 (a - 3)}$

Step 2

To write $\frac{a^{2}}{a - 3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{a^{2}}{a - 3} \cdot \frac{5}{5} - \frac{4}{5 (a - 3)}$

Step 3

Write each expression with a common denominator of $(a - 3) \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{a^{2}}{a - 3}$ by $\frac{5}{5}$ .

$\frac{a^{2} \cdot 5}{(a - 3) \cdot 5} - \frac{4}{5 (a - 3)}$

Step 3.2

Reorder the factors of $(a - 3) \cdot 5$ .

$\frac{a^{2} \cdot 5}{5 (a - 3)} - \frac{4}{5 (a - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{a^{2} \cdot 5 - 4}{5 (a - 3)}$

Step 5

Move $5$ to the left of $a^{2}$ .

$\frac{5 a^{2} - 4}{5 (a - 3)}$