help! how can you simplify sqrt of (a^-2-m^-2)

Question

anonymous · Answer

pict of the eq

anonymous · Answer

The step of going from (a^-2 - m^-2) to (a-m)^-2 is not valid.

It's similar to a binomial squaring.

(x+y)^2 is not equal to x^2 + y^2
Rather, it's equal to x^2 + 2xy + y^2

anonymous · Answer

so can you help me what to do with the equation?

anonymous · Answer

I'm not really sure how much simplifying you can really do... I mean all I can think of is combining it into one fraction? Is that considered simpler?

anonymous · Answer

$$\sqrt{\frac{1}{a^{2}}-\frac{1}{m^{2}}}=\sqrt{\frac{m^{2}-a^{2}}{a^{2}m^{2}}}=\frac{1}{am}\sqrt{m^{2}-a^{2}}$$

anonymous · Answer

That's all I can think of..

anonymous · Answer

combining like? sqrt of (1/a^2-b^2)?

anonymous · Answer

thank you so much! :) that was the answer! :)

anonymous · Answer

yep, just make a common denominator and squish it all together.