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How do you simplify #7 /(x-5)-(2+x)/(x-5)#?

Answer 1

Julia Adams

# 7/(x-5) - (2+x)/(x-5)#

here, the denominators are common

adding the numerators # (7 - (2+x))/(x-5)#

# (7 - 2-x)/(x-5)#

# = (5-x)/(x-5)# # = cancel(5-x)/-cancel((5-x))#

# = color(red)(-1#

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Answer 2

Hazel Anglin

To simplify the expression 7/(x-5) - (2+x)/(x-5), we can combine the two fractions by finding a common denominator. The common denominator in this case is (x-5).

So, the expression can be simplified as follows:

7/(x-5) - (2+x)/(x-5) = (7 - (2+x))/(x-5) = (7 - 2 - x)/(x-5) = (5 - x)/(x-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.