Solve v/a+1/1-a

$$\frac { v } { a } + \frac { 1 } { 1 - a }$$

Evaluate

$$\frac{a+v-av}{a\left(1-a\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 1-a is a\left(-a+1\right). Multiply \frac{v}{a} times \frac{-a+1}{-a+1}. Multiply \frac{1}{1-a} times \frac{a}{a}.

$$\frac{v\left(-a+1\right)}{a\left(-a+1\right)}+\frac{a}{a\left(-a+1\right)}$$

Since \frac{v\left(-a+1\right)}{a\left(-a+1\right)} and \frac{a}{a\left(-a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{v\left(-a+1\right)+a}{a\left(-a+1\right)}$$

Do the multiplications in v\left(-a+1\right)+a.

$$\frac{-va+v+a}{a\left(-a+1\right)}$$

Expand a\left(-a+1\right).

$$\frac{-va+v+a}{-a^{2}+a}$$

Differentiate w.r.t. v

$$\frac{1}{a}$$