This is the proof to the first Math Proof Problem of the Week.

**Proof **

Squaring $latex \frac{a +b}{a – b}$ results to

$latex \displaystyle \frac{a^2 + 2ab + b^2}{a^2-2ab + b^2}$

Now, since.

Since $latex a^2 + b^2 = 6$,

$latex \displaystyle \frac{a^2 + 2ab + b^2}{a^2-2ab + b^2} = \frac{6ab + 2ab}{6ab – 2ab} = \frac{8ab}{2ab} = 2$.

This means that

$latex \displaystyle \frac{a + b}{a – b} = \pm \sqrt{2}$

Now, since $latex a > b > 0$, $latex a – b$ is positive, which means that

$latex \displaystyle\frac{a + b}{a – b}$

is positive.

Therefore, $latex \frac{a + b}{a – b} = \sqrt{2}$