Is it possible to isolate this variable from this equation?

Question

Can someone with strong knowledge of math answer me?

I need to isolate $x$ from this equation:

$a = \dfrac{b((1+x)^n - 1)}{ x(1 + x)^n}$

Answer 1

It's impossible to fully isolate $x$ because there will always be some $x$ either to the power of $n$ or to the root of $n$, but here's as far as you can go:

Let's begin by dividing both sides by $b$:

$$\frac{a}{b} = \frac{(1+x)^n - 1}{ x(1 + x)^n}$$

Break the right side into two fractions:

$$\frac{a}{b} = \frac{(1+x)^n}{ x(1 + x)^n} - \frac{1}{ x(1 + x)^n}$$

Simplify the first fraction on the right:

$$\frac{a}{b} = \frac{1}{x} - \frac{1}{x(1 + x)^n}$$

I think it's impossible to make any progress after that.