Question

√a +2√y
√a-2√y

Do you know how to rationalize the denominator and simply?

Answer 1

`(a+4√(ay)+y )/(a-4y )`

Explanation:

As far as I understand, it looks like this:
`(√(a)+2√(y) )/(√(a)-2√(y) )`

We know that:

1. 
   `(a - b)*(a + b) = a^(2) -b^(2)`
2. we can always multiply by 1
3. 
   `(√(a)+2√(y) )/(√(a) +2√(y) )=1`
4. 
   `(a+b)^2=a^2+2ab+b^2`

Therefore,

`(√(a)+2√(y) )/(√(a)-2√(y) ) *1 =(√(a)+2√(y) )/(√(a)-2√(y) ) *(√(a) +2√(y) )/(√(a)+2√(y) ) =((√(a)+2√(y))^2 )/((√(a))^2-(2√(y))^2 ) =(a+4√(ay)+y )/(a-4y )`

Answer 2

`(a+4√(ay)+4y )/(a-4y)`

given:

`(√(a)+2√(y))/(√(a)-2√(y) )`

solve for:

Rationalized denominator

Explanation:

1. Rationalize the denominator

`(√(a)+2√(y))/(√(a)-2√(y) ) * (2√(y) )/(2√(y) )`

2. Simplify

`(2√(y)(√(a)+2√(y) ) )/(2√(y)(√(a)-2√(y)) )`

`(a+4√(ay)+4y )/(a-4y)`