How to solve for $x$ in $\frac{200}{x+10} = \frac{200}{x} -1$?

Question

I am really confused how to calculate the following. The answer is $40$, but what are the steps to get $40$? $$\frac{200}{x+10} = \frac{200}{x} - 1.$$ Thank you.

Answer 1

Hint: Just multiply everything by $x(x+10)$ to clear the denominators. Then solve the quadratic equation you get. There are two possible answers...

Answer 2

$$\begin{align}{200 \over x + 10} &= {200 - x \over x} \\ \\ \\ 200x &=(x + 10)(200 - x) \\ \\ \\ 200x&=-x^2 + 190x + 2000 \\ \\ \\ x^2 + 10x - 2000&=0\end{align} $$Solve the quadratic equation and you get your solutions.