Solve for a g=(1+2a)/a ; for a

$g = \frac{1 + 2 a}{a}$ ; for $a$

Step 1

Rewrite the equation as $\frac{1 + 2 a}{a} = g$ .

$\frac{1 + 2 a}{a} = g$

Step 2

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.

$a, 1$

The LCM of one and any expression is the expression.

$a$

Step 3

Multiply each term in $\frac{1 + 2 a}{a} = g$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{1 + 2 a}{a} = g$ by $a$ .

$\frac{1 + 2 a}{a} a = g a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{1 + 2 a}{a} a = g a$

Rewrite the expression.

$1 + 2 a = g a$

Step 4

Solve the equation.

Subtract $g a$ from both sides of the equation.

$1 + 2 a - g a = 0$

Subtract $1$ from both sides of the equation.

$2 a - g a = - 1$

Factor $a$ out of $2 a - g a$ .

Factor $a$ out of $2 a$ .

$a \cdot 2 - g a = - 1$

Factor $a$ out of $- g a$ .

$a \cdot 2 + a (- g) = - 1$

Factor $a$ out of $a \cdot 2 + a (- g)$ .

$a (2 - g) = - 1$

Divide each term in $a (2 - g) = - 1$ by $2 - g$ and simplify.

Divide each term in $a (2 - g) = - 1$ by $2 - g$ .

$\frac{a (2 - g)}{2 - g} = \frac{- 1}{2 - g}$

Simplify the left side.

Cancel the common factor of $2 - g$ .

Cancel the common factor.

$\frac{a (2 - g)}{2 - g} = \frac{- 1}{2 - g}$

Divide $a$ by $1$ .

$a = \frac{- 1}{2 - g}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{1}{2 - g}$