Anyone good at Rational Expressions?

Question

I remember learning about Rational Expressions but thats been over a year ago and now I can't seem to figure them out!
please help!



1)
(x/y)-(y/x)
--------------
(1/y)+(1/x)

2)
(a/b)+(c/d)
---------------
(b/a)+(d/c)

3)
(a/b)-(c/d)
--------------
(b/a)-(d/c)




Thanks for any help!

Answer 1

1)
(x/y)-(y/x)
--------------
(1/y)+(1/x)

= [(x^2 - y^2)/xy] * [xy/(x + y)]
= (x - y) (x + y) / (x + y)
= x - y

2)
(a/b)+(c/d)
---------------
(b/a)+(d/c)
= [(ad + bc)/bd]/[(bc + ad)/ac]
= [(ad + bc) * ac]/[ bd * (ad + bc)]
= ac/bd

3)
(a/b)-(c/d)
--------------
(b/a)-(d/c)
= [(ad - bc)/bd]/[(bc - ad)/ac]
= [(ad - bc)ac]/[bd(bc - ad)]