Finite Math Examples

$\frac{1 - \frac{2 x}{y}}{\frac{1}{x} + \frac{x}{y}}$

Step 1

Multiply the numerator and denominator of the fraction by $y x$ .

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Step 1.1

Multiply $\frac{1 - \frac{2 x}{y}}{\frac{1}{x} + \frac{x}{y}}$ by $\frac{y x}{y x}$ .

$\frac{y x}{y x} \cdot \frac{1 - \frac{2 x}{y}}{\frac{1}{x} + \frac{x}{y}}$

Step 1.2

Combine.

$\frac{y x (1 - \frac{2 x}{y})}{y x (\frac{1}{x} + \frac{x}{y})}$

Step 2

Apply the distributive property.

$\frac{y x \cdot 1 + y x (- \frac{2 x}{y})}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $y$ .

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Step 3.1.1

Move the leading negative in $- \frac{2 x}{y}$ into the numerator.

$\frac{y x \cdot 1 + y x \frac{- 2 x}{y}}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.1.2

Factor $y$ out of $y x$ .

$\frac{y x \cdot 1 + y (x) \frac{- 2 x}{y}}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.1.3

Cancel the common factor.

$\frac{y x \cdot 1 + y x \frac{- 2 x}{y}}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.1.4

Rewrite the expression.

$\frac{y x \cdot 1 + x (- 2 x)}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.2

Raise $x$ to the power of $1$ .

$\frac{y x \cdot 1 - 2 (x^{1} x)}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.3

Raise $x$ to the power of $1$ .

$\frac{y x \cdot 1 - 2 (x^{1} x^{1})}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y x \cdot 1 - 2 x^{1 + 1}}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.5

Add $1$ and $1$ .

$\frac{y x \cdot 1 - 2 x^{2}}{y x \frac{1}{x} + y x \frac{x}{y}}$

Step 3.6

Cancel the common factor of $x$ .

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Step 3.6.1

Factor $x$ out of $y x$ .

$\frac{y x \cdot 1 - 2 x^{2}}{x y \frac{1}{x} + y x \frac{x}{y}}$

Step 3.6.2

Cancel the common factor.

$\frac{y x \cdot 1 - 2 x^{2}}{x y \frac{1}{x} + y x \frac{x}{y}}$

Step 3.6.3

Rewrite the expression.

$\frac{y x \cdot 1 - 2 x^{2}}{y + y x \frac{x}{y}}$

Step 3.7

Cancel the common factor of $y$ .

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Step 3.7.1

Factor $y$ out of $y x$ .

$\frac{y x \cdot 1 - 2 x^{2}}{y + y (x) \frac{x}{y}}$

Step 3.7.2

Cancel the common factor.

$\frac{y x \cdot 1 - 2 x^{2}}{y + y x \frac{x}{y}}$

Step 3.7.3

Rewrite the expression.

$\frac{y x \cdot 1 - 2 x^{2}}{y + x \cdot x}$

Step 3.8

Raise $x$ to the power of $1$ .

$\frac{y x \cdot 1 - 2 x^{2}}{y + x^{1} x}$

Step 3.9

Raise $x$ to the power of $1$ .

$\frac{y x \cdot 1 - 2 x^{2}}{y + x^{1} x^{1}}$

Step 3.10

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y x \cdot 1 - 2 x^{2}}{y + x^{1 + 1}}$

Step 3.11

Add $1$ and $1$ .

$\frac{y x \cdot 1 - 2 x^{2}}{y + x^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $y x \cdot 1 - 2 x^{2}$ .

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Step 4.1.1

Factor $x$ out of $y x \cdot 1$ .

$\frac{x (y \cdot 1) - 2 x^{2}}{y + x^{2}}$

Step 4.1.2

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

$\frac{x (y \cdot 1) + x (- 2 x)}{y + x^{2}}$

Step 4.1.3

Factor $x$ out of $x (y \cdot 1) + x (- 2 x)$ .

$\frac{x (y \cdot 1 - 2 x)}{y + x^{2}}$

Step 4.2

Multiply $y$ by $1$ .

$\frac{x (y - 2 x)}{y + x^{2}}$