Solve for v 3u=(5+7v)/(v-3)

$3 u = \frac{5 + 7 v}{v - 3}$

Step 1

Multiply the equation by $v - 3$ .

$(v - 3) (3 u) = (\frac{5 + 7 v}{v - 3}) (v - 3)$

Step 2

Simplify the left side.

Simplify $(v - 3) (3 u)$ .

Apply the distributive property.

$v (3 u) - 3 (3 u) = (\frac{5 + 7 v}{v - 3}) (v - 3)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$3 v u - 3 (3 u) = (\frac{5 + 7 v}{v - 3}) (v - 3)$

Multiply $3$ by $- 3$ .

$3 v u - 9 u = (\frac{5 + 7 v}{v - 3}) (v - 3)$

Step 3

Simplify the right side.

Cancel the common factor of $v - 3$ .

Cancel the common factor.

$3 v u - 9 u = \frac{5 + 7 v}{v - 3} (v - 3)$

Rewrite the expression.

$3 v u - 9 u = 5 + 7 v$

Step 4

Solve for $v$ .

Subtract $7 v$ from both sides of the equation.

$3 v u - 9 u - 7 v = 5$

Add $9 u$ to both sides of the equation.

$3 v u - 7 v = 5 + 9 u$

Factor $v$ out of $3 v u - 7 v$ .

Factor $v$ out of $3 v u$ .

$v (3 u) - 7 v = 5 + 9 u$

Factor $v$ out of $- 7 v$ .

$v (3 u) + v \cdot - 7 = 5 + 9 u$

Factor $v$ out of $v (3 u) + v \cdot - 7$ .

$v (3 u - 7) = 5 + 9 u$

Divide each term in $v (3 u - 7) = 5 + 9 u$ by $3 u - 7$ and simplify.

Divide each term in $v (3 u - 7) = 5 + 9 u$ by $3 u - 7$ .

$\frac{v (3 u - 7)}{3 u - 7} = \frac{5}{3 u - 7} + \frac{9 u}{3 u - 7}$

Simplify the left side.

Cancel the common factor of $3 u - 7$ .

Cancel the common factor.

$\frac{v (3 u - 7)}{3 u - 7} = \frac{5}{3 u - 7} + \frac{9 u}{3 u - 7}$

Divide $v$ by $1$ .

$v = \frac{5}{3 u - 7} + \frac{9 u}{3 u - 7}$

Simplify the right side.

Combine the numerators over the common denominator.

$v = \frac{5 + 9 u}{3 u - 7}$

Solve for v 3u=(5+7v)/(v-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.