Solve a+b=a/x+y

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b\left(x+y\right)}{x+y-1}\text{, }&x\neq 1-y\text{ and }x\neq -y\\a\in \mathrm{C}\text{, }&x=1-y\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+y.

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

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

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

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

$$xa+ya+xb+yb=a$$

Subtract a from both sides.

$$xa+ya+xb+yb-a=0$$

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

$$xa+ya+yb-a=-xb$$

Subtract yb from both sides.

$$xa+ya-a=-xb-yb$$

Reorder the terms.

$$ax+ay-a=-bx-by$$

Combine all terms containing a.

$$\left(x+y-1\right)a=-bx-by$$

Divide both sides by x+y-1.

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

Dividing by x+y-1 undoes the multiplication by x+y-1.

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{b\left(x+y\right)}{x+y-1}\text{, }&x\neq 1-y\text{ and }x\neq -y\\a\in \mathrm{R}\text{, }&x=1-y\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+y.

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

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

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

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

$$xa+ya+xb+yb=a$$

Subtract a from both sides.

$$xa+ya+xb+yb-a=0$$

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

$$xa+ya+yb-a=-xb$$

Subtract yb from both sides.

$$xa+ya-a=-xb-yb$$

Reorder the terms.

$$ax+ay-a=-bx-by$$

Combine all terms containing a.

$$\left(x+y-1\right)a=-bx-by$$

Divide both sides by x+y-1.

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

Dividing by x+y-1 undoes the multiplication by x+y-1.

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

Solve for b

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

$$x\neq -y$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+y.

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

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

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

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

$$xa+ya+xb+yb=a$$

Subtract xa from both sides.

$$ya+xb+yb=a-xa$$

Subtract ya from both sides.

$$xb+yb=a-xa-ya$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by x+y.

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

Dividing by x+y undoes the multiplication by x+y.

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