/sci/ - Science & Math

>>9569423
I don't understand at all how I'm supposed to get 2 on the right hand side, while getting the numerator on the left hand side.

In aimless attempts at striking gold with algebraic guesswork, I found a common denominator for the fractions on the right hand side, and was left with a fraction of the form [math] \frac{x_1 ^2 (y_1 ^2 + y_2 ^2) + y_1^2(x_1 ^2 + x_2 ^2)}{(x_1 ^2 + x_2 ^2)(y_1 ^2 + y_2 ^2)} [/math].

I understand from the top answer here:
>https://math.stackexchange.com/questions/1329759/michael-spivaks-calculus-chapter-1-problem-19

That the numerator can be factored further, but I take issue with the top answer for two reasons:
1) The denominator was not squared as it should've been, since we begin with x^2 + y^2, where x is an atrocious fraction with a square root in the denominator.
2) The notation is not something that Spivak has covered yet, and while I understand summation notation somewhat, the indexing was a bit off putting as it doesn't sync up with Spivak's answer (I also prefer to approach text in a self-contained fashion, using only what has been given).

There's must be some algebraic tricks lying here somewhere, but how do I find them?