Equation with fractions

Question

If $P=\frac{h}{1-h}$ then $h$ is equal to? Answer is: $\frac{P}{1+P}$ I understand that $\frac{P}{1+P}$ is the right answer for when I replace $\frac{P}{1+P}$ for h the answer solves the equation, but what I can't do is find the answer by myself, how do I get to $\frac{P}{1+P}$?

Answer 1

$$P = \frac{h}{1-h}$$

Cross-multiplying you get

$$(1-h) \cdot P = h$$

After this, simply work to get the expression in terms of h.

$$P - P\cdot h = h$$

$$P = h + P \cdot h$$

$$P = (1 + P) \cdot h \implies h = \frac{P}{1 + P}$$

Answer 2

Hint: Multiply both sides by $1-h$ and solve for $h$. This tactic (multiplying by the denominator) works in many cases when you want to solve problems with variables in the denominator; in the future it should be one of the first things you try.

Answer 3

P = h/1-h --> (1-h)P = h; P - Ph = h; P = h + Ph; P = h(1 + P); P/(1+P) = h