Originally Posted by

**sammy28** hello to all.

this happens to be a surd but could equally apply to any algebraic equation involving fractions.

ive been asked to solve the following in the form $\displaystyle A\sqrt{B}+C$, where A, B and C are rational numbers.

$\displaystyle \frac{1}{\sqrt{2}}+x = \frac{x}{\sqrt{2}}$

my question is given any algebraic fraction should you always begin by multiplying the denominator?

because i get two answers depending on which way i go but only one is in the requested format, and thats the one that multiplies the denominator to start with, eg:

$\displaystyle \frac{\sqrt{2}}{\sqrt{2}} + \sqrt{2}x = \frac{\sqrt{2}x}{\sqrt{2}}$

$\displaystyle 1 = x - x\sqrt{2}$

$\displaystyle 1 = x(1 - \sqrt{2})$

----------------

**ERROR HERE**

$\displaystyle x = -1-\sqrt{2}$

----------------------------

**correct one**

$\displaystyle 1 = x(1 - \sqrt{2})$

Divide both sides by $\displaystyle (1 - \sqrt{2})$

$\displaystyle x= 1/(1 - \sqrt{2})$