Solve for a n=b/a+3

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

Step 1

Rewrite the equation as $\frac{b}{a} + 3 = n$ .

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

Step 2

Subtract $3$ from both sides of the equation.

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

Step 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.

$a, 1, 1$

The LCM of one and any expression is the expression.

$a$

Step 4

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

Multiply each term in $\frac{b}{a} = n - 3$ by $a$ .

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

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

$b = n a - 3 a$

Step 5

Solve the equation.

Rewrite the equation as $n a - 3 a = b$ .

$n a - 3 a = b$

Factor $a$ out of $n a - 3 a$ .

Factor $a$ out of $n a$ .

$a n - 3 a = b$

Factor $a$ out of $- 3 a$ .

$a n + a \cdot - 3 = b$

Factor $a$ out of $a n + a \cdot - 3$ .

$a (n - 3) = b$

Divide each term in $a (n - 3) = b$ by $n - 3$ and simplify.

Divide each term in $a (n - 3) = b$ by $n - 3$ .

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

Simplify the left side.

Cancel the common factor of $n - 3$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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