Finite Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $2 y - 1$ .

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $2 y - 1$ .

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Step 3.1.1

Move the leading negative in $- \frac{y}{2 y - 1}$ into the numerator.

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 4

Simplify the denominator.

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Step 4.1

Multiply $2 y - 1$ by $1$ .

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

Step 4.2

Subtract $y$ from $2 y$ .

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

Step 5

Simplify the numerator.

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Step 5.1

Raise $2 y - 1$ to the power of $1$ .

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

Step 5.2

Raise $2 y - 1$ to the power of $1$ .

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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