Solve a+b/b=phi

$$\frac { a + b } { b } = \phi$$

Solve for a

$$a=b\left(ϕ-1\right)$$

$$b\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$a+b=ϕb$$

Subtract b from both sides.

$$a=ϕb-b$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{a}{1-ϕ}\text{, }&a\neq 0\text{ and }ϕ\neq 1\\b\neq 0\text{, }&a=0\text{ and }ϕ=1\end{matrix}\right.$$

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 b.

$$a+b=ϕb$$

Subtract ϕb from both sides.

$$a+b-ϕb=0$$

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

$$b-ϕb=-a$$

Combine all terms containing b.

$$\left(1-ϕ\right)b=-a$$

Divide both sides by 1-ϕ.

$$\frac{\left(1-ϕ\right)b}{1-ϕ}=-\frac{a}{1-ϕ}$$

Dividing by 1-ϕ undoes the multiplication by 1-ϕ.

$$b=-\frac{a}{1-ϕ}$$

Variable b cannot be equal to 0.

$$b=-\frac{a}{1-ϕ}\text{, }b\neq 0$$