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How do you simplify #5 / (2(x-5)) + (3x) / (x-5)#?

Answer 1

#(5+6x)/(2(x-5)#

Notes that the denominator in both elements of the expression contain #(x-5)# which is therefore a common factor. The expression can be written as #(1/(x-5))(5/2+3x)# #=(1/(x-5))(5+6x)/2#

#=(5+6x)/(2(x-5)#

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Answer 2

Eva Abramson

To simplify the expression 5 / (2(x-5)) + (3x) / (x-5), we need to find a common denominator and combine the fractions. The common denominator is (x-5).

To add the fractions, we multiply the numerator and denominator of the first fraction by 2, and the numerator and denominator of the second fraction by 1:

(5 * 2) / (2(x-5)) + (3x * 1) / (x-5)

This simplifies to:

10 / (2(x-5)) + 3x / (x-5)

Now, we can combine the fractions by adding the numerators:

(10 + 3x) / (2(x-5))

Therefore, the simplified expression is (10 + 3x) / (2(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.