Question

x^-1 + y^-1
-----------
3x^-2 +5y^-2
please show me the steps and final answer, thanks.

Answer 1

Step 1 top line: add the two fractions 1/x and 1/y (you should get (x+y)/xy

Step 2 bottom line: add the two fractions 3/x^2 and 5/y^2 to get (5x^2 + 3y^2)/x^2y^2

You should be OK from here

Answer 2

Remember when dividing by a fraction to turn it upside down and multiply, then cancel what you can and you're done

Answer 3

So I'm getting my final answer to be:
x+y
---
8

Answer 4

Pretty sure thats wrong though...

Answer 5

mmmm...I get Step1 divided by Step 2

(x+y)/xy divided by (5x^2 + 3y^2)/x^2y^2

which is (inverting the bottom fraction) (x+y)/xy multiplied by x^2y^2/(5x^2 + 3y^2)

cancel the xy top and bottom to get

xy(x+y)/(5x^2 + 3y^2)

let me know if you agree

Answer 6

So you're getting
X+Y
---
5X^2+3Y^2
?

Answer 7

No, top line is xy(x+y). Bottom line is OK

Answer 8

Wouldn't that factor out on the top then?

Answer 9

Not quite sure what you mean by 'factor out', but no, there's nothing more you can cancel or do. You could multiply out the top line as \[x^2y + xy^2\] if you want, but I assume you are to factor out fully so my answer is still \[xy(x+y)/(5x^2+3y^2)\]

Answer 10

Alright, thank you.