How do you combine #1/2+2/(x+2)#?

Answer 1

#(x+6)/(2x+4)#

A fraction consists of

#("numerator")/("denominator") -> ("count")/("size indicator of what you are counting")#
#color(blue)("Important fact 1")# You can not DIRECTLY add or subtract the counts unless the size indicators are the same
#color(blue)("Important fact 2")# Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way numbers look but not change their actual value. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)([1/2color(red)(xx1)]+[2/(x+2)color(red)(xx1)]#

Is the same as:

#color(blue)([1/2color(red)(xx(x+2)/(x+2))]+[2/(x+2)color(red)(xx2/2)] #
#(x+2)/(2(x+2))+4/(2(x+2))#
#(x+2+4)/(2(x+2)) " "=" "(x+6)/(2x+4)#
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Answer 2

To combine 1/2 + 2/(x+2), we need to find a common denominator. The common denominator in this case is 2(x+2).

To convert 1/2 to have the same denominator, we multiply the numerator and denominator by (x+2), resulting in (x+2)/(2(x+2)).

To convert 2/(x+2) to have the same denominator, we multiply the numerator and denominator by 2, resulting in 4/(2(x+2)).

Now that both fractions have the same denominator, we can combine them by adding their numerators: (x+2)/(2(x+2)) + 4/(2(x+2)).

Combining the numerators gives us (x+2+4)/(2(x+2)).

Simplifying the numerator gives us (x+6)/(2(x+2)).

Therefore, 1/2 + 2/(x+2) can be combined as (x+6)/(2(x+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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