Solve for u r=(s-t)/(u-8)

$r = \frac{s - t}{u - 8}$

Step 1

Rewrite the equation as $\frac{s - t}{u - 8} = r$ .

$\frac{s - t}{u - 8} = r$

Step 2

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.

$u - 8, 1$

Remove parentheses.

$u - 8, 1$

The LCM of one and any expression is the expression.

$u - 8$

Step 3

Multiply each term in $\frac{s - t}{u - 8} = r$ by $u - 8$ to eliminate the fractions.

Multiply each term in $\frac{s - t}{u - 8} = r$ by $u - 8$ .

$\frac{s - t}{u - 8} (u - 8) = r (u - 8)$

Simplify the left side.

Cancel the common factor of $u - 8$ .

Cancel the common factor.

$\frac{s - t}{u - 8} (u - 8) = r (u - 8)$

Rewrite the expression.

$s - t = r (u - 8)$

Simplify the right side.

Apply the distributive property.

$s - t = r u + r \cdot - 8$

Move $- 8$ to the left of $r$ .

$s - t = r u - 8 r$

Step 4

Solve the equation.

Rewrite the equation as $r u - 8 r = s - t$ .

$r u - 8 r = s - t$

Add $8 r$ to both sides of the equation.

$r u = s - t + 8 r$

Divide each term in $r u = s - t + 8 r$ by $r$ and simplify.

Divide each term in $r u = s - t + 8 r$ by $r$ .

$\frac{r u}{r} = \frac{s}{r} + \frac{- t}{r} + \frac{8 r}{r}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r u}{r} = \frac{s}{r} + \frac{- t}{r} + \frac{8 r}{r}$

Divide $u$ by $1$ .

$u = \frac{s}{r} + \frac{- t}{r} + \frac{8 r}{r}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$u = \frac{s}{r} - \frac{t}{r} + \frac{8 r}{r}$

Cancel the common factor of $r$ .

Cancel the common factor.

$u = \frac{s}{r} - \frac{t}{r} + \frac{8 r}{r}$

Divide $8$ by $1$ .

$u = \frac{s}{r} - \frac{t}{r} + 8$

Solve for u r=(s-t)/(u-8)

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