Solve in Terms of the Arbitrary Variable U T=(9R)/(S+U)

$T = \frac{9 R}{S + U}$

Step 1

Solve the equation for $R$ .

Rewrite the equation as $\frac{9 R}{S + U} = T$ .

$\frac{9 R}{S + U} = T$

Multiply both sides by $S + U$ .

$\frac{9 R}{S + U} (S + U) = T (S + U)$

Simplify.

Simplify the left side.

Cancel the common factor of $S + U$ .

Cancel the common factor.

$\frac{9 R}{S + U} (S + U) = T (S + U)$

Rewrite the expression.

$9 R = T (S + U)$

Simplify the right side.

Simplify $T (S + U)$ .

Apply the distributive property.

$9 R = T S + T U$

Reorder $T$ and $S$ .

$9 R = S T + T U$

Divide each term in $9 R = S T + T U$ by $9$ and simplify.

Divide each term in $9 R = S T + T U$ by $9$ .

$\frac{9 R}{9} = \frac{S T}{9} + \frac{T U}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 R}{9} = \frac{S T}{9} + \frac{T U}{9}$

Divide $R$ by $1$ .

$R = \frac{S T}{9} + \frac{T U}{9}$

Step 2

Solve the equation for $S$ .

Rewrite the equation as $\frac{9 (\frac{S T}{9} + \frac{T U}{9})}{S + U} = T$ .

$\frac{9 (\frac{S T}{9} + \frac{T U}{9})}{S + U} = T$

Factor each term.

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{9 \frac{S T + T U}{9}}{S + U} = T$

Factor $T$ out of $S T + T U$ .

Factor $T$ out of $S T$ .

$\frac{9 \frac{T S + T U}{9}}{S + U} = T$

Factor $T$ out of $T U$ .

$\frac{9 \frac{T S + T (U)}{9}}{S + U} = T$

Factor $T$ out of $T S + T (U)$ .

$\frac{9 \frac{T (S + U)}{9}}{S + U} = T$

Combine $9$ and $\frac{T (S + U)}{9}$ .

$\frac{\frac{9 (T (S + U))}{9}}{S + U} = T$

Remove parentheses.

$\frac{\frac{9 T (S + U)}{9}}{S + U} = T$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{9 T (S + U)}{9}$ by cancelling the common factors.

Cancel the common factor.

$\frac{\frac{9 T (S + U)}{9}}{S + U} = T$

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=(9R)/(S+U)

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