Solve in Terms of the Arbitrary Variable u t=(4r)/(s+u)

$t = \frac{4 r}{s + u}$

Step 1

Solve the equation for $r$ .

Rewrite the equation as $\frac{4 r}{s + u} = t$ .

$\frac{4 r}{s + u} = t$

Multiply both sides by $s + u$ .

$\frac{4 r}{s + u} (s + u) = t (s + u)$

Simplify.

Simplify the left side.

Cancel the common factor of $s + u$ .

Cancel the common factor.

$\frac{4 r}{s + u} (s + u) = t (s + u)$

Rewrite the expression.

$4 r = t (s + u)$

Simplify the right side.

Simplify $t (s + u)$ .

Apply the distributive property.

$4 r = t s + t u$

Reorder $t$ and $s$ .

$4 r = s t + t u$

Divide each term in $4 r = s t + t u$ by $4$ and simplify.

Divide each term in $4 r = s t + t u$ by $4$ .

$\frac{4 r}{4} = \frac{s t}{4} + \frac{t u}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r}{4} = \frac{s t}{4} + \frac{t u}{4}$

Divide $r$ by $1$ .

$r = \frac{s t}{4} + \frac{t u}{4}$

Step 2

Solve the equation for $s$ .

Rewrite the equation as $\frac{4 (\frac{s t}{4} + \frac{t u}{4})}{s + u} = t$ .

$\frac{4 (\frac{s t}{4} + \frac{t u}{4})}{s + u} = t$

Factor each term.

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{4 \frac{s t + t u}{4}}{s + u} = t$

Factor $t$ out of $s t + t u$ .

Factor $t$ out of $s t$ .

$\frac{4 \frac{t s + t u}{4}}{s + u} = t$

Factor $t$ out of $t u$ .

$\frac{4 \frac{t s + t (u)}{4}}{s + u} = t$

Factor $t$ out of $t s + t (u)$ .

$\frac{4 \frac{t (s + u)}{4}}{s + u} = t$

Combine $4$ and $\frac{t (s + u)}{4}$ .

$\frac{\frac{4 (t (s + u))}{4}}{s + u} = t$

Remove parentheses.

$\frac{\frac{4 t (s + u)}{4}}{s + u} = t$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{4 t (s + u)}{4}$ by cancelling the common factors.

Cancel the common factor.

$\frac{\frac{4 t (s + u)}{4}}{s + u} = t$

Rewrite the expression.

$\frac{\frac{t (s + u)}{1}}{s + u} = t$

Divide $t (s + u)$ by $1$ .

$\frac{t (s + u)}{s + u} = t$

Cancel the common factor of $s + u$ .

Cancel the common factor.

$\frac{t (s + u)}{s + u} = t$

Divide $t$ by $1$ .

$t = t$

Solve the equation.

Move all terms containing $t$ to the left side of the equation.

Subtract $t$ from both sides of the equation.

$t - t = 0$

Subtract $t$ from $t$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true

Solve in Terms of the Arbitrary Variable u t=(4r)/(s+u)

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