Solve for y (x+y)/z-a=b

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

Step 1

Simplify $\frac{x + y}{z} - a$ .

To write $- a$ as a fraction with a common denominator, multiply by $\frac{z}{z}$ .

$\frac{x + y}{z} - a \cdot \frac{z}{z} = b$

Combine $- a$ and $\frac{z}{z}$ .

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

Combine the numerators over the common denominator.

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

Step 2

Multiply both sides by $z$ .

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

Step 3

Simplify the left side.

Simplify $\frac{x + y - a z}{z} z$ .

Cancel the common factor of $z$ .

Cancel the common factor.

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

Rewrite the expression.

$x + y - a z = b z$

Simplify the expression.

Move $y$ .

$x - a z + y = b z$

Reorder $x$ and $- a z$ .

$- a z + x + y = b z$

Step 4

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

Add $a z$ to both sides of the equation.

$x + y = b z + a z$

Subtract $x$ from both sides of the equation.

$y = b z + a z - x$