How do you rationalize the denominator and simplify #5/(sqrt[3] + sqrt[5])#?

Answer 1

#=color(blue)((-5(sqrt3-sqrt5))/2#

Rationalizing involves multiplying the numerator and the denominator of the expression by the conjugate of the denominator.

The conjugate of the denominator is #sqrt3+sqrt5 = color(blue)(sqrt3-sqrt5#

Rationalizing

#5/(sqrt3+sqrt5)= (5* color(blue)((sqrt3-sqrt5)))/((sqrt3+sqrt5)* color(blue)((sqrt3-sqrt5))#
The denominator can be simplified by applying the property #(a+b)(a-b) = a^2-b^2#
So, #(sqrt3+sqrt5)* (sqrt3-sqrt5)=3-5=color(blue)(-2#

The expression then becomes:

#(5sqrt3-5sqrt5)/color(blue)(-2#
#=color(blue)((5(sqrt3-sqrt5))/-2#
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Answer 2

To rationalize the denominator and simplify 5/(sqrt[3] + sqrt[5]), we multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt[3] - sqrt[5]). This results in (5 * (sqrt[3] - sqrt[5])) / ((sqrt[3] + sqrt[5]) * (sqrt[3] - sqrt[5])). Simplifying further, we get (5 * sqrt[3] - 5 * sqrt[5]) / (3 - 5). This simplifies to (-5 * sqrt[5] + 5 * sqrt[3]) / (-2).

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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.

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.

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.

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.

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