Finite Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $a^{2}$ .

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $a$ .

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Step 3.1.1

Factor $a$ out of $a^{2}$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $a^{2}$ .

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Step 3.2.1

Move the leading negative in $- \frac{3}{a^{2}}$ into the numerator.

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.3

Cancel the common factor of $a^{2}$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

Cancel the common factor of $a$ .

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Step 3.4.1

Factor $a$ out of $a^{2}$ .

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

Step 3.4.2

Cancel the common factor.

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

Step 3.4.3

Rewrite the expression.

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

Step 4

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

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

Step 5

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

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