Solve for a 5/(a+b)=3

$\frac{5}{a + b} = 3$

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.

$a + b, 1$

Remove parentheses.

$a + b, 1$

The LCM of one and any expression is the expression.

$a + b$

Multiply each term in $\frac{5}{a + b} = 3$ by $a + b$ to eliminate the fractions.

Multiply each term in $\frac{5}{a + b} = 3$ by $a + b$ .

$\frac{5}{a + b} (a + b) = 3 (a + b)$

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

$\frac{5}{a + b} (a + b) = 3 (a + b)$

Rewrite the expression.

$5 = 3 (a + b)$

Simplify the right side.

Apply the distributive property.

$5 = 3 a + 3 b$

Solve the equation.

Rewrite the equation as $3 a + 3 b = 5$ .

$3 a + 3 b = 5$

Subtract $3 b$ from both sides of the equation.

$3 a = 5 - 3 b$

Divide each term in $3 a = 5 - 3 b$ by $3$ and simplify.

Divide each term in $3 a = 5 - 3 b$ by $3$ .

$\frac{3 a}{3} = \frac{5}{3} + \frac{- 3 b}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{5}{3} + \frac{- 3 b}{3}$

Divide $a$ by $1$ .

$a = \frac{5}{3} + \frac{- 3 b}{3}$

Simplify the right side.

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3 b$ .

$a = \frac{5}{3} + \frac{3 (- b)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$a = \frac{5}{3} + \frac{3 (- b)}{3 (1)}$

Cancel the common factor.

$a = \frac{5}{3} + \frac{3 (- b)}{3 \cdot 1}$

Rewrite the expression.

$a = \frac{5}{3} + \frac{- b}{1}$

Divide $- b$ by $1$ .

$a = \frac{5}{3} - b$

Solve for a 5/(a+b)=3

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