This is from my physics homework. It has to do with the relativistic doppler effect. I've simplified it.
They claim that
A: (1/sqrt(1-(x^2)))*sqrt((1+x)/(1-x))
is equal to
B: 1/(1-x)
How do they go from A to B?
This is from my physics homework. It has to do with the relativistic doppler effect. I've simplified it.
They claim that
A: (1/sqrt(1-(x^2)))*sqrt((1+x)/(1-x))
is equal to
B: 1/(1-x)
How do they go from A to B?
$\displaystyle \frac{1}{\sqrt{1-x^2}}\cdot\sqrt{\frac{1+x}{1-x}}=\frac{1}{\sqrt{(1+x)(1-x)}}\cdot\sqrt{\frac{1+x}{1-x}}=\frac{1}{\sqrt{1-x}}\cdot\sqrt{\frac{1}{1-x}}=\frac{1}{\sqrt{(1-x)^2}}=\frac{1}{|1-x|}$
Since we must have $\displaystyle x<1$ for the original expression to be defined, this simplifies to:
$\displaystyle \frac{1}{1-x}$