Please help with simplifying [ (sqrt(x) + sqrt(y))^2] / [ (x - y) / (sqrt(1/y) + 3 sqrt(1/x)) ] divided by...

[Alex398]

I am unable to come forward with this expression. These are the steps i take at first but i am doing something wrong...

Thank you for your help!

 

[Dr.Peterson]

View attachment 35684
I am unable to come forward with this expression. These are the steps i take at first but i am doing something wrong...
View attachment 35685
Thank you for your help!

Why do you think anything is wrong? Just keep doing as you are doing.

I would simplify the two expressions with radicals in the denominators by using the common denominator. Then some more things will cancel; then, if the goal is to eliminate all radicals from the denominator, you can use conjugates.

Is there any indication as to what would be considered "simple" enough?

 

[khansaheb]

View attachment 35684
I am unable to come forward with this expression. These are the steps i take at first but i am doing something wrong...
View attachment 35685
Thank you for your help!

I would try substitution

m = √x......... and n = √y

and do some algebra.

 

[Steven G]

You are doing fine. Just continue.