Solve for x x/a-1=y/b

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

Step 1

Subtract $\frac{y}{b}$ from both sides of the equation.

$\frac{x}{a} - 1 - \frac{y}{b} = 0$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

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

Add $\frac{y}{b}$ to both sides of the equation.

$\frac{x}{a} = 1 + \frac{y}{b}$

Step 3

Multiply both sides by $a$ .

$\frac{x}{a} a = (1 + \frac{y}{b}) a$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{x}{a} a = (1 + \frac{y}{b}) a$

Rewrite the expression.

$x = (1 + \frac{y}{b}) a$

Simplify the right side.

Simplify $(1 + \frac{y}{b}) a$ .

Apply the distributive property.

$x = 1 a + \frac{y}{b} a$

Multiply $a$ by $1$ .

$x = a + \frac{y}{b} a$

Combine $\frac{y}{b}$ and $a$ .

$x = a + \frac{y a}{b}$

Simplify with commuting.

Reorder $y$ and $a$ .

$x = a + \frac{a y}{b}$

Reorder $a$ and $\frac{a y}{b}$ .

$x = \frac{a y}{b} + a$