Solve for r (n-p)/(r-5)=m

$\frac{n - p}{r - 5} = m$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$r - 5, 1$

Remove parentheses.

$r - 5, 1$

The LCM of one and any expression is the expression.

$r - 5$

Step 2

Multiply each term in $\frac{n - p}{r - 5} = m$ by $r - 5$ to eliminate the fractions.

Multiply each term in $\frac{n - p}{r - 5} = m$ by $r - 5$ .

$\frac{n - p}{r - 5} (r - 5) = m (r - 5)$

Simplify the left side.

Cancel the common factor of $r - 5$ .

Cancel the common factor.

$\frac{n - p}{r - 5} (r - 5) = m (r - 5)$

Rewrite the expression.

$n - p = m (r - 5)$

Simplify the right side.

Apply the distributive property.

$n - p = m r + m \cdot - 5$

Move $- 5$ to the left of $m$ .

$n - p = m r - 5 m$

Step 3

Solve the equation.

Rewrite the equation as $m r - 5 m = n - p$ .

$m r - 5 m = n - p$

Add $5 m$ to both sides of the equation.

$m r = n - p + 5 m$

Divide each term in $m r = n - p + 5 m$ by $m$ and simplify.

Divide each term in $m r = n - p + 5 m$ by $m$ .

$\frac{m r}{m} = \frac{n}{m} + \frac{- p}{m} + \frac{5 m}{m}$

Simplify the left side.

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{m r}{m} = \frac{n}{m} + \frac{- p}{m} + \frac{5 m}{m}$

Divide $r$ by $1$ .

$r = \frac{n}{m} + \frac{- p}{m} + \frac{5 m}{m}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$r = \frac{n}{m} - \frac{p}{m} + \frac{5 m}{m}$

Cancel the common factor of $m$ .

Cancel the common factor.

$r = \frac{n}{m} - \frac{p}{m} + \frac{5 m}{m}$

Divide $5$ by $1$ .

$r = \frac{n}{m} - \frac{p}{m} + 5$

Solve for r (n-p)/(r-5)=m

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