How to find x from the equation $\sqrt{x + \sqrt{x}} - \sqrt{x - \sqrt{x}} = m \sqrt{\frac{x}{x+\sqrt{x}}}$ For m are real number,
Find x from the equation
$$\sqrt{x + \sqrt{x}} - \sqrt{x - \sqrt{x}} = m \sqrt{\frac{x}{x+\sqrt{x}}}$$
I tried to multiply $\sqrt{x + \sqrt{x}}$ to the both sides and I get
$$x + \sqrt{x} - \sqrt{x^{2} - x} = m \sqrt{x}$$
What should I do now to get x? Can anyone show me a hint please?

As you got (for $x\neq0$):
$$ x+\sqrt{x} + \sqrt{x^2-x} = m\sqrt{x} $$
$$ x+\sqrt{x} + \sqrt{x}\sqrt{x-1} = m\sqrt{x} $$
Setting $ u = \sqrt{x} $ ($ u\neq0 $) we get:
$$ u^2+u+u\sqrt{u^2-1} = mu $$
$$ u+1+\sqrt{u^2-1} = m $$
$$ \sqrt{u^2-1} = (m-1) - u$$
Squaring both sides:
$$ u^2-1 = (m-1)^2-2u(m-1)+u^2 $$
We get:
$$ u = \frac{(m-1)^2+1}{2(m-1)} $$
where $m\neq1$ and $x$ becomes:
$$ x = \Bigg(\frac{(m-1)^2+1}{2(m-1)}\Bigg)^2 $$
