Precalculus Examples

$\frac{5 p}{2 q - p} + \frac{10 q}{p - 2 q}$

Step 1

Set the denominator in $\frac{5 p}{2 q - p}$ equal to $0$ to find where the expression is undefined.

$2 q - p = 0$

Step 2

Solve for $p$ .

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Step 2.1

Subtract $2 q$ from both sides of the equation.

$- p = - 2 q$

Step 2.2

Divide each term in $- p = - 2 q$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- p = - 2 q$ by $- 1$ .

$\frac{- p}{- 1} = \frac{- 2 q}{- 1}$

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.

$\frac{p}{1} = \frac{- 2 q}{- 1}$

Step 2.2.2.2

Divide $p$ by $1$ .

$p = \frac{- 2 q}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

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

$p = - 1 \cdot (- 2 q)$

Step 2.2.3.2

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

$p = - (- 2 q)$

Step 2.2.3.3

Multiply $- 2$ by $- 1$ .

$p = 2 q$

Step 3

Set the denominator in $\frac{10 q}{p - 2 q}$ equal to $0$ to find where the expression is undefined.

$p - 2 q = 0$

Step 4

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

$p = 2 q$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${p | p \in ℝ}$