Question

Simplify the complex fraction

(1/x - 1/y^2) / (1/x^2y - 1/xy^2)

Answer 1

\[\frac{ \frac{ 1 }{ x } - \frac{ 1 }{ y ^{2} }}{ \frac{ 1 }{ x ^{2}y } - \frac{ 1 }{ xy ^{2} } }\]

Answer 2

Look at the denominator. I/x is a factor of both terms in the denominator. So factorise the denominator and you are nearly there!

Answer 3

So just factor them for right now ?

Answer 4

Yes. Can you do it?

Answer 5

Yes hold on a second, Im doing the math right now

Answer 6

Sure :)

Answer 7

@kropot72 I'm not really getting anything :/

Answer 8

Putting the numerator terms over a common denominator:
\[\frac{1}{x}-\frac{1}{y ^{2}}=\frac{y ^{2}-x}{xy ^{2}}.............(1)\]
Putting the denominator terms over a common denominator:
\[\frac{1}{x ^{2}y}-\frac{1}{xy ^{2}}=\frac{y-x}{x ^{2}y ^{2}}...........(2)\]
Dividing (1) by (2) gives:
\[\frac{xy ^{2}-x ^{2}}{y-x}\]

Answer 9

Is that the answer or is there more simplifying to do?

Answer 10

I can't simplify it further.

Answer 11

Well in the back of the book it says the answer is x so maybe they simplified the y-x ?

Answer 12

Are you sure the question has been copied correctly?

Answer 13

Im pretty sure it is.... hold on, ill see if another textbook has the same question or something

Answer 14

Thank you. I really want to help!

Answer 15

Okay so I looked on the online book and it says it is 1/xy not 1/x

Answer 16

And thanks, I appreciate the help (: @kropot72

Answer 17

You're welcome. Sorry, I have reached a dead end :(

Answer 18

It's fine, I think I can figure it out now, thank you for your help!

Answer 19

You're welcome :)