Basic Math Examples

$\frac{\frac{9}{4} + 2}{\frac{10}{a} - 3}$

Step 1

Multiply the numerator and denominator of the fraction by $4 a$ .

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Step 1.1

Multiply $\frac{\frac{9}{4} + 2}{\frac{10}{a} - 3}$ by $\frac{4 a}{4 a}$ .

$\frac{4 a}{4 a} \cdot \frac{\frac{9}{4} + 2}{\frac{10}{a} - 3}$

Step 1.2

Combine.

$\frac{4 a (\frac{9}{4} + 2)}{4 a (\frac{10}{a} - 3)}$

Step 2

Apply the distributive property.

$\frac{4 a \frac{9}{4} + 4 a \cdot 2}{4 a \frac{10}{a} + 4 a \cdot - 3}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $4 a$ .

$\frac{4 (a) \frac{9}{4} + 4 a \cdot 2}{4 a \frac{10}{a} + 4 a \cdot - 3}$

Step 3.1.2

Cancel the common factor.

$\frac{4 a \frac{9}{4} + 4 a \cdot 2}{4 a \frac{10}{a} + 4 a \cdot - 3}$

Step 3.1.3

Rewrite the expression.

$\frac{a \cdot 9 + 4 a \cdot 2}{4 a \frac{10}{a} + 4 a \cdot - 3}$

Step 3.2

Cancel the common factor of $a$ .

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Step 3.2.1

Factor $a$ out of $4 a$ .

$\frac{a \cdot 9 + 4 a \cdot 2}{a \cdot 4 \frac{10}{a} + 4 a \cdot - 3}$

Step 3.2.2

Cancel the common factor.

$\frac{a \cdot 9 + 4 a \cdot 2}{a \cdot 4 \frac{10}{a} + 4 a \cdot - 3}$

Step 3.2.3

Rewrite the expression.

$\frac{a \cdot 9 + 4 a \cdot 2}{4 \cdot 10 + 4 a \cdot - 3}$

Step 3.3

Multiply $4$ by $10$ .

$\frac{a \cdot 9 + 4 a \cdot 2}{40 + 4 a \cdot - 3}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $a$ out of $a \cdot 9 + 4 a \cdot 2$ .

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Step 4.1.1

Factor $a$ out of $a \cdot 9$ .

$\frac{a (9) + 4 a \cdot 2}{40 + 4 a \cdot - 3}$

Step 4.1.2

Factor $a$ out of $4 a \cdot 2$ .

$\frac{a (9) + a (4 \cdot 2)}{40 + 4 a \cdot - 3}$

Step 4.1.3

Factor $a$ out of $a (9) + a (4 \cdot 2)$ .

$\frac{a (9 + 4 \cdot 2)}{40 + 4 a \cdot - 3}$

Step 4.2

Multiply $4$ by $2$ .

$\frac{a (9 + 8)}{40 + 4 a \cdot - 3}$

Step 4.3

Add $9$ and $8$ .

$\frac{a \cdot 17}{40 + 4 a \cdot - 3}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $- 3$ by $4$ .

$\frac{a \cdot 17}{40 - 12 a}$

Step 5.2

Factor $4$ out of $40 - 12 a$ .

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Step 5.2.1

Factor $4$ out of $40$ .

$\frac{a \cdot 17}{4 (10) - 12 a}$

Step 5.2.2

Factor $4$ out of $- 12 a$ .

$\frac{a \cdot 17}{4 (10) + 4 (- 3 a)}$

Step 5.2.3

Factor $4$ out of $4 (10) + 4 (- 3 a)$ .

$\frac{a \cdot 17}{4 (10 - 3 a)}$

Step 6

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

$\frac{17 a}{4 (10 - 3 a)}$