Question

Rationalize the denominator of :

1/ (√3 - √2 + 1)​

Answer 1

Answer:

1

 

Rationalize the denominator: \frac{1}{\sqrt{3}-\sqrt{2}+1} \cdot \frac{\sqrt{3}-\sqrt{2}-1}{\sqrt{3}-\sqrt{2}-1}=\frac{\sqrt{3}-\sqrt{2}-1}{3-\sqrt{6}-\sqrt{3}-\sqrt{6}+2+\sqrt{2}+\sqrt{3}-\sqrt{2}-1}3−2+11⋅3−2−13−2−1=3−6−3−6+2+2+3−2−13−2−1.

\frac{\sqrt{3}-\sqrt{2}-1}{3-\sqrt{6}-\sqrt{3}-\sqrt{6}+2+\sqrt{2}+\sqrt{3}-\sqrt{2}-1}3−6−3−6+2+2+3−2−13−2−1

2

 

Collect like terms.

\frac{\sqrt{3}-\sqrt{2}-1}{(3+2-1)+(-\sqrt{6}-\sqrt{6})+(-\sqrt{3}+\sqrt{3})+(\sqrt{2}-\sqrt{2})}(3+2−1)+(−6−6)+(−3+3