Precalculus Examples

$\frac{a^{3} - b^{3}}{{(a - b)}^{2}} + \frac{3 a b}{b - a}$

Step 1

Set the denominator in $\frac{a^{3} - b^{3}}{{(a - b)}^{2}}$ equal to $0$ to find where the expression is undefined.

${(a - b)}^{2} = 0$

Step 2

Solve for $a$ .

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Step 2.1

Set the $a - b$ equal to $0$ .

$a - b = 0$

Step 2.2

Add $b$ to both sides of the equation.

$a = b$

Step 3

Set the denominator in $\frac{3 a b}{b - a}$ equal to $0$ to find where the expression is undefined.

$b - a = 0$

Step 4

Solve for $a$ .

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Step 4.1

Subtract $b$ from both sides of the equation.

$- a = - b$

Step 4.2

Divide each term in $- a = - b$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- a = - b$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- b}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- b}{- 1}$

Step 4.2.2.2

Divide $a$ by $1$ .

$a = \frac{- b}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Dividing two negative values results in a positive value.

$a = \frac{b}{1}$

Step 4.2.3.2

Divide $b$ by $1$ .

$a = b$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${a | a \in ℝ}$