Basic Math Examples

$\frac{4 + a}{a - 3} + \frac{4}{5}$

Step 1

To write $\frac{4 + a}{a - 3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{a - 3}{a - 3}$ .

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

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 $\frac{4 + a}{a - 3}$ by $\frac{5}{5}$ .

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

Step 3.2

Multiply $\frac{4}{5}$ by $\frac{a - 3}{a - 3}$ .

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

Step 3.3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Rewrite $\frac{(4 + a) \cdot 5 + 4 (a - 3)}{5 (a - 3)}$ in a factored form.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $4$ by $5$ .

$\frac{20 + a \cdot 5 + 4 (a - 3)}{5 (a - 3)}$

Step 5.3

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

$\frac{20 + 5 a + 4 (a - 3)}{5 (a - 3)}$

Step 5.4

Apply the distributive property.

$\frac{20 + 5 a + 4 a + 4 \cdot - 3}{5 (a - 3)}$

Step 5.5

Multiply $4$ by $- 3$ .

$\frac{20 + 5 a + 4 a - 12}{5 (a - 3)}$

Step 5.6

Subtract $12$ from $20$ .

$\frac{5 a + 4 a + 8}{5 (a - 3)}$

Step 5.7

Add $5 a$ and $4 a$ .

$\frac{9 a + 8}{5 (a - 3)}$