Solve for a b/a=c+3b

$\frac{b}{a} = c + 3 b$

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.

$a, 1, 1$

The LCM of one and any expression is the expression.

$a$

Step 2

Multiply each term in $\frac{b}{a} = c + 3 b$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{b}{a} = c + 3 b$ by $a$ .

$\frac{b}{a} a = c a + 3 b a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{b}{a} a = c a + 3 b a$

Rewrite the expression.

$b = c a + 3 b a$

Step 3

Solve the equation.

Rewrite the equation as $c a + 3 b a = b$ .

$c a + 3 b a = b$

Factor $a$ out of $c a + 3 b a$ .

Factor $a$ out of $c a$ .

$a c + 3 b a = b$

Factor $a$ out of $3 b a$ .

$a c + a (3 b) = b$

Factor $a$ out of $a c + a (3 b)$ .

$a (c + 3 b) = b$

Divide each term in $a (c + 3 b) = b$ by $c + 3 b$ and simplify.

Divide each term in $a (c + 3 b) = b$ by $c + 3 b$ .

$\frac{a (c + 3 b)}{c + 3 b} = \frac{b}{c + 3 b}$

Simplify the left side.

Cancel the common factor of $c + 3 b$ .

Cancel the common factor.

$\frac{a (c + 3 b)}{c + 3 b} = \frac{b}{c + 3 b}$

Divide $a$ by $1$ .

$a = \frac{b}{c + 3 b}$