Precalculus Examples

$\frac{b^{2} - 4 b y}{2 y^{2} - b y} - \frac{4 y}{b - 2 y}$

Step 1

Set the denominator in $\frac{b^{2} - 4 b y}{2 y^{2} - b y}$ equal to $0$ to find where the expression is undefined.

$2 y^{2} - b y = 0$

Step 2

Solve for $b$ .

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Step 2.1

Subtract $2 y^{2}$ from both sides of the equation.

$- b y = - 2 y^{2}$

Step 2.2

Divide each term in $- b y = - 2 y^{2}$ by $- y$ and simplify.

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Step 2.2.1

Divide each term in $- b y = - 2 y^{2}$ by $- y$ .

$\frac{- b y}{- y} = \frac{- 2 y^{2}}{- y}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{b y}{y} = \frac{- 2 y^{2}}{- y}$

Step 2.2.2.2

Cancel the common factor of $y$ .

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Step 2.2.2.2.1

Cancel the common factor.

$\frac{b y}{y} = \frac{- 2 y^{2}}{- y}$

Step 2.2.2.2.2

Divide $b$ by $1$ .

$b = \frac{- 2 y^{2}}{- y}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of $y^{2}$ and $y$ .

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Step 2.2.3.1.1

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

$b = \frac{y (- 2 y)}{- y}$

Step 2.2.3.1.2

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$b = - 1 \cdot (- 2 y)$

Step 2.2.3.2

Simplify the expression.

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Step 2.2.3.2.1

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$b = - (- 2 y)$

Step 2.2.3.2.2

Multiply $- 2$ by $- 1$ .

$b = 2 y$

Step 3

Set the denominator in $\frac{4 y}{b - 2 y}$ equal to $0$ to find where the expression is undefined.

$b - 2 y = 0$

Step 4

Add $2 y$ to both sides of the equation.

$b = 2 y$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${b | b \in ℝ}$