Square of sum: Equations with Variables on One Side

Look at the following equation:

$\frac{\sqrt{x}-\sqrt{x+1}}{x+1}=1$

This can also be written as:

$x[A(x+B)-x^3]=0$

Calculate A and B.

B=1 , A=4

Solve the following equation:

$\frac{1}{(x+1)^2}+\frac{1}{x+1}=1$

$-\frac{1}{2}[1\pm\sqrt{5}\rbrack$

Look at the following equation:

$\frac{\sqrt{x}+\sqrt{x+1}}{x+1}=1$

The same equation can be presented as follows:

$x[A(x+B)-x^3]=0$

Calculate A and B.

B=1 , A=4