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How do you rationalize the denominator and simplify #6/(2sqrtx+sqrty)#?

Answer 1

Ethan Adkins

#(6(2sqrt(x)-sqrt(y)))/(4x-y)#

Multiplying numerator and denominator by #2sqrt(x)-sqrt(y)# we get

#(6(sqrt(x)-sqrt(y)))/(4x-y)# using that #(a-b)(a+b)=a^2-b^2#

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Answer 2

Ethan Adkins

To rationalize the denominator and simplify the expression 6/(2√x + √y), you can multiply both the numerator and denominator by the conjugate of the denominator, which is 2√x - √y. This will eliminate the square roots in the denominator. The simplified expression will be (6 * (2√x - √y)) / ((2√x + √y) * (2√x - √y)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.