Finite Math Examples

$\frac{9 a}{5 a - 10} - \frac{a - 3}{a - 2}$

Step 1

Factor $5$ out of $5 a - 10$ .

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Step 1.1

Factor $5$ out of $5 a$ .

$\frac{9 a}{5 (a) - 10} - \frac{a - 3}{a - 2}$

Step 1.2

Factor $5$ out of $- 10$ .

$\frac{9 a}{5 a + 5 \cdot - 2} - \frac{a - 3}{a - 2}$

Step 1.3

Factor $5$ out of $5 a + 5 \cdot - 2$ .

$\frac{9 a}{5 (a - 2)} - \frac{a - 3}{a - 2}$

Step 2

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

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

Step 3

Write each expression with a common denominator of $5 (a - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Reorder the factors of $(a - 2) \cdot 5$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $- 1$ by $- 3$ .

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

Step 5.3

Apply the distributive property.

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

Step 5.4

Multiply $5$ by $- 1$ .

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

Step 5.5

Multiply $3$ by $5$ .

$\frac{9 a - 5 a + 15}{5 (a - 2)}$

Step 5.6

Subtract $5 a$ from $9 a$ .

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