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?

Squaring both sides we get $$x+\sqrt{x}+x-\sqrt{x}-2\sqrt{x^2-x}=\frac{m^2x}{x+\sqrt{x}}$$
Simplifying we get
$$2x-\frac{m^2x}{x+\sqrt{x}}=2\sqrt{x^2-x}$$
simplifying we get
$$m^4x^2=-4x(x^2+x+2x\sqrt{x})$$ diviniding by $$x\neq 0$$ $$4x+4+m^4=-8\sqrt{x}$$ squaring again
$$16x^2-32x+8xm^4+8m^4+m^8+16=0$$
Can you solve this equation?
