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How do you simplify #[(2)/(4-x)] + [(5)/(x-4)]#?

Answer 1

Avery Alexander

#2/(4-x)+5/(x-4) =3/(x-4)#

#2/(4-x)+5/(x-4)#

#= 2/-(x-4)+5/(x-4)#

#=(-1*2)/(-1*-(x-4))+5/(x-4)#

#=(-2)/(x-4)+5/(x-4)#

#=(-2+5)/(x-4)#

#=3/(x-4)#

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Answer 2

Jace Anderson

To simplify [(2)/(4-x)] + [(5)/(x-4)], we need to find a common denominator and combine the fractions. The common denominator is (4-x)(x-4).

Multiplying the first fraction by (x-4)/(x-4) and the second fraction by (4-x)/(4-x), we get:

[(2(x-4))/((4-x)(x-4))] + [(5(4-x))/((4-x)(x-4))]

Expanding and combining the numerators, we have:

[(2x-8+20-5x)/((4-x)(x-4))]

Simplifying the numerator, we get:

[(-3x+12)/((4-x)(x-4))]

Therefore, the simplified expression is (-3x+12)/((4-x)(x-4)).

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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.