Solve for x x/a-2x=b

$\frac{x}{a} - 2 x = b$

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 $\frac{x}{a} - 2 x = b$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{x}{a} - 2 x = b$ by $a$ .

$\frac{x}{a} a - 2 x a = b a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{x}{a} a - 2 x a = b a$

Rewrite the expression.

$x - 2 x a = b a$

Step 3

Solve the equation.

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

Raise $x$ to the power of $1$ .

$x - 2 x a = b a$

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - 2 x a = b a$

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

$x \cdot 1 + x (- 2 a) = b a$

Factor $x$ out of $x \cdot 1 + x (- 2 a)$ .

$x (1 - 2 a) = b a$

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

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

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

Simplify the left side.

Cancel the common factor of $1 - 2 a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$x = \frac{b a}{1 - 2 a}$