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How do you simplify #sqrt (x-2) +5 / sqrt(x-2#?

Answer 1

Eva Abramson

You need to put on a common denominator.

#=(sqrt(x - 2) xx sqrt(x - 2) + 5)/(sqrt(x - 2))#

#=(x - 2 + 5)/(sqrt(x - 2))#

#=(x + 3)/(sqrt(x - 2))#

You will want to rationalize the denominator now:

#=(x + 3)/sqrt(x - 2) xx sqrt(x - 2)/sqrt(x - 2)#

#=((x + 3)(sqrt(x - 2)))/(x - 2)#

Hopefully this helps!

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Answer 2

Jace Anderson

To simplify the expression (sqrt(x-2) + 5) / sqrt(x-2), we can rationalize the denominator. By multiplying both the numerator and denominator by the conjugate of the denominator, which is sqrt(x-2) - 5, we eliminate the square root in the denominator. This results in the simplified expression of 1 + 5 / (sqrt(x-2) - 5).

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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.