Calculus Examples

$- p r - 2 r + 15 = 0$

Step 1

Subtract $15$ from both sides of the equation.

$- p r - 2 r = - 15$

Step 2

Factor $r$ out of $- p r - 2 r$ .

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Step 2.1

Factor $r$ out of $- p r$ .

$r (- p) - 2 r = - 15$

Step 2.2

Factor $r$ out of $- 2 r$ .

$r (- p) + r \cdot - 2 = - 15$

Step 2.3

Factor $r$ out of $r (- p) + r \cdot - 2$ .

$r (- p - 2) = - 15$

Step 3

Divide each term in $r (- p - 2) = - 15$ by $- p - 2$ and simplify.

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Step 3.1

Divide each term in $r (- p - 2) = - 15$ by $- p - 2$ .

$\frac{r (- p - 2)}{- p - 2} = \frac{- 15}{- p - 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- p - 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{r (- p - 2)}{- p - 2} = \frac{- 15}{- p - 2}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 15}{- p - 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$r = - \frac{15}{- p - 2}$

Step 3.3.2

Factor $- 1$ out of $- p$ .

$r = - \frac{15}{- (p) - 2}$

Step 3.3.3

Rewrite $- 2$ as $- 1 (2)$ .

$r = - \frac{15}{- (p) - 1 (2)}$

Step 3.3.4

Factor $- 1$ out of $- (p) - 1 (2)$ .

$r = - \frac{15}{- (p + 2)}$

Step 3.3.5

Simplify the expression.

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Step 3.3.5.1

Rewrite $- (p + 2)$ as $- 1 (p + 2)$ .

$r = - \frac{15}{- 1 (p + 2)}$

Step 3.3.5.2

Move the negative in front of the fraction.

$r = - - \frac{15}{p + 2}$

Step 3.3.5.3

Multiply $- 1$ by $- 1$ .

$r = 1 \frac{15}{p + 2}$

Step 3.3.5.4

Multiply $\frac{15}{p + 2}$ by $1$ .

$r = \frac{15}{p + 2}$