Question

In the simplest form, (1/x^2)-(1/y^2) / (1/x)+(1/y) is equivalent to...

Answer 1

That's nice, but that is NOT what is written.

If you mean \(\dfrac{\dfrac{1}{x^{2}} - \dfrac{1}{y^{2}}}{\dfrac{1}{x} - \dfrac{1}{y}}\), you need still more parenthes.

\(\dfrac{\dfrac{1}{x^{2}} - \dfrac{1}{y^{2}}}{\dfrac{1}{x} - \dfrac{1}{y}} = \dfrac{\left(\dfrac{1}{x} + \dfrac{1}{y}\right)\cdot\left(\dfrac{1}{x} - \dfrac{1}{y}\right)}{\dfrac{1}{x} - \dfrac{1}{y}} = \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{x+y}{xy}\)

@ehuman wandered off in a couple of places.

Answer 2

@tkhunny we both made errors. the denominator is + not - I started right, looking for where I failed to copy the correct sign...

Answer 3

Good call. That is hard to copy without LaTex.

Answer 4

It's still \(\dfrac{y-x}{xy}\)

Answer 5

deleting my errors so as not to confuse the OP