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How do you rationalize the denominator and simplify #7/(sqrtx+sqrty)#?

Answer 1

#7(sqrtx-sqrty)/(x-y)#

Multiply both numerator and denominator by the conjugate of the denominator #sqrtx-sqrty# and use #(a^2-b^2)=\(a-b)(a+b)#

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Answer 2

Avery Alexander

To rationalize the denominator and simplify the expression 7/(√x + √y), we can multiply both the numerator and denominator by the conjugate of the denominator, which is (√x - √y). This will eliminate the square roots in the denominator.

By applying the conjugate, the expression becomes:

7/(√x + √y) * (√x - √y)/(√x - √y)

Expanding the numerator and denominator, we get:

(7√x - 7√y)/(√x√x - √x√y + √x√y - √y√y)

Simplifying further:

(7√x - 7√y)/(x - y)

Therefore, the rationalized and simplified form of 7/(√x + √y) is (7√x - 7√y)/(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.