(3√x) / (2√x-√y)?

Question

Simplify after performing indicated operations.

I agree with the first one. I have no idea what Ravi is talking about, though. How can you just change the sign, and multiply instead of divide?

Answer 1

(3√x) / (2√x-√y), rationalise them
(3√x) / (2√x-√y) * (2√x + √y) / (2√x + √y)
(3√x ) * (2√x + √y) / [(2√x - √y) * (2√x + √y)]
(2√x - √y) * (2√x + √y) is in the form of (a+b)(a-b) = a^2 - b^2
(6x + 3√x √y) / [ (2√x)^2 - (√y) ^2

(6x + 3√x √y) / ( 4 x - y)
should be your final answer

Answer 2

(3√x) / (2√x - √y) =
(3√x)(2√x + √y) / (2√x - √y)(2√x + √y) =
(6x + √xy) / (4x - y)

Answer 3

(3x^1/2 ) / (2x^1/2 - y^1/2)
rationalise i.e multiply by Dr x ^ = x root
(3x^1/2 ) . (2x^1/2 + y^1/2)
...............................................
(2x^1/2 - y^1/2). (2x^1/2 + y^1/2)

= 6x + 3(xy)^1/2
.....................................
(2x^1/2)^2 - (y^1/2)^2 becoz, (a+b)(a-b) = (a^2 - b^2)

= 6x + 3(xy)^1/2
.......................
4x - y