Basic Math Examples

$\frac{\frac{5}{x} + \frac{3}{x^{2}}}{\frac{25}{x^{2}} - \frac{9}{x}}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{5}{x} + \frac{3}{x^{2}}}{\frac{25}{x^{2}} - \frac{9}{x}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{x^{2}}{x^{2}} \cdot \frac{\frac{5}{x} + \frac{3}{x^{2}}}{\frac{25}{x^{2}} - \frac{9}{x}}$

Step 1.2

Combine.

$\frac{x^{2} (\frac{5}{x} + \frac{3}{x^{2}})}{x^{2} (\frac{25}{x^{2}} - \frac{9}{x})}$

Step 2

Apply the distributive property.

$\frac{x^{2} \frac{5}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

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

$\frac{x \cdot x \frac{5}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.1.2

Cancel the common factor.

$\frac{x \cdot x \frac{5}{x} + x^{2} \frac{3}{x^{2}}}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.1.3

Rewrite the expression.

$\frac{x \cdot 5 + x^{2} \frac{3}{x^{2}}}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

$\frac{x \cdot 5 + x^{2} \frac{3}{x^{2}}}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.2.2

Rewrite the expression.

$\frac{x \cdot 5 + 3}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.3

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

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Step 3.3.1

Cancel the common factor.

$\frac{x \cdot 5 + 3}{x^{2} \frac{25}{x^{2}} + x^{2} (- \frac{9}{x})}$

Step 3.3.2

Rewrite the expression.

$\frac{x \cdot 5 + 3}{25 + x^{2} (- \frac{9}{x})}$

Step 3.4

Cancel the common factor of $x$ .

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Step 3.4.1

Move the leading negative in $- \frac{9}{x}$ into the numerator.

$\frac{x \cdot 5 + 3}{25 + x^{2} \frac{- 9}{x}}$

Step 3.4.2

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

$\frac{x \cdot 5 + 3}{25 + x \cdot x \frac{- 9}{x}}$

Step 3.4.3

Cancel the common factor.

$\frac{x \cdot 5 + 3}{25 + x \cdot x \frac{- 9}{x}}$

Step 3.4.4

Rewrite the expression.

$\frac{x \cdot 5 + 3}{25 + x \cdot - 9}$

Step 4

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

$\frac{5 x + 3}{25 + x \cdot - 9}$

Step 5

Move $- 9$ to the left of $x$ .

$\frac{5 x + 3}{25 - 9 x}$