Solve x+a/a=y+b/b

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

Solve for a

$$\left\{\begin{matrix}a=\frac{bx}{y}\text{, }&x\neq 0\text{ and }b\neq 0\text{ and }y\neq 0\\a\neq 0\text{, }&x=0\text{ and }y=0\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\left(x+a\right)=a\left(y+b\right)$$

Use the distributive property to multiply b by x+a.

$$bx+ba=a\left(y+b\right)$$

Use the distributive property to multiply a by y+b.

$$bx+ba=ay+ab$$

Subtract ay from both sides.

$$bx+ba-ay=ab$$

Subtract ab from both sides.

$$bx+ba-ay-ab=0$$

Combine ba and -ab to get 0.

$$bx-ay=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$-ay=-bx$$

Cancel out -1 on both sides.

$$ay=bx$$

The equation is in standard form.

$$ya=bx$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{bx}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{bx}{y}$$

Variable a cannot be equal to 0.

$$a=\frac{bx}{y}\text{, }a\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ay}{x}\text{, }&y\neq 0\text{ and }a\neq 0\text{ and }x\neq 0\\b\neq 0\text{, }&y=0\text{ and }x=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\left(x+a\right)=a\left(y+b\right)$$

Use the distributive property to multiply b by x+a.

$$bx+ba=a\left(y+b\right)$$

Use the distributive property to multiply a by y+b.

$$bx+ba=ay+ab$$

Subtract ab from both sides.

$$bx+ba-ab=ay$$

Combine ba and -ab to get 0.

$$bx=ay$$

The equation is in standard form.

$$xb=ay$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ay}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ay}{x}$$

Variable b cannot be equal to 0.

$$b=\frac{ay}{x}\text{, }b\neq 0$$