Precalculus Examples

$\frac{a}{2 a - b} + \frac{3 a - b}{b - 2 a}$

Step 1

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

$2 a - b = 0$

Step 2

Solve for $a$ .

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Step 2.1

Add $b$ to both sides of the equation.

$2 a = b$

Step 2.2

Divide each term in $2 a = b$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 a = b$ by $2$ .

$\frac{2 a}{2} = \frac{b}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{b}{2}$

Step 2.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{b}{2}$

Step 3

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

$b - 2 a = 0$

Step 4

Solve for $a$ .

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Step 4.1

Subtract $b$ from both sides of the equation.

$- 2 a = - b$

Step 4.2

Divide each term in $- 2 a = - b$ by $- 2$ and simplify.

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Step 4.2.1

Divide each term in $- 2 a = - b$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- b}{- 2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- b}{- 2}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- b}{- 2}$

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.

$a = \frac{b}{2}$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${a | a \in ℝ}$