Precalculus Examples

$\frac{8 a + 4 b}{2 a b + b^{2} - 2 a d - b d}$

Step 1

Set the denominator in $\frac{8 a + 4 b}{2 a b + b^{2} - 2 a d - b d}$ equal to $0$ to find where the expression is undefined.

$2 a b + b^{2} - 2 a d - b d = 0$

Step 2

Solve for $a$ .

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Step 2.1

Move all terms not containing $a$ to the right side of the equation.

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Step 2.1.1

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

$2 a b - 2 a d - b d = - b^{2}$

Step 2.1.2

Add $b d$ to both sides of the equation.

$2 a b - 2 a d = - b^{2} + b d$

Step 2.2

Factor $2 a$ out of $2 a b - 2 a d$ .

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Step 2.2.1

Factor $2 a$ out of $2 a b$ .

$2 a (b) - 2 a d = - b^{2} + b d$

Step 2.2.2

Factor $2 a$ out of $- 2 a d$ .

$2 a (b) + 2 a (- 1 d) = - b^{2} + b d$

Step 2.2.3

Factor $2 a$ out of $2 a (b) + 2 a (- 1 d)$ .

$2 a (b - 1 d) = - b^{2} + b d$

Step 2.3

Rewrite $- 1 d$ as $- d$ .

$2 a (b - d) = - b^{2} + b d$

Step 2.4

Divide each term in $2 a (b - d) = - b^{2} + b d$ by $2 (b - d)$ and simplify.

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Step 2.4.1

Divide each term in $2 a (b - d) = - b^{2} + b d$ by $2 (b - d)$ .

$\frac{2 a (b - d)}{2 (b - d)} = \frac{- b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{2 a (b - d)}{2 (b - d)} = \frac{- b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 2.4.2.1.2

Rewrite the expression.

$\frac{a (b - d)}{b - d} = \frac{- b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 2.4.2.2

Cancel the common factor of $b - d$ .

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Step 2.4.2.2.1

Cancel the common factor.

$\frac{a (b - d)}{b - d} = \frac{- b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 2.4.2.2.2

Divide $a$ by $1$ .

$a = \frac{- b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Move the negative in front of the fraction.

$a = - \frac{b^{2}}{2 (b - d)} + \frac{b d}{2 (b - d)}$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${a | a \in ℝ}$