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How do you write #4/(x+2)+3/(x-2)# as a single fraction in its simplest form?

Answer 1

Eva Abramson

The answer is #=(7x-2)/(x^2-4)#

#(a+b)(a-b)=a^2-b^2#

The common denominator is #=(x+2)(x-2)#

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

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

#=(4x-8+3x+6)/(x^2-4)#

#=(7x-2)/(x^2-4)#

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Answer 2

Genesis Allen

To write 4/(x+2)+3/(x-2) as a single fraction in its simplest form, we need to find a common denominator for the two fractions. The common denominator is (x+2)(x-2).

Multiplying the first fraction by (x-2)/(x-2) and the second fraction by (x+2)/(x+2), we get:

(4(x-2))/((x+2)(x-2)) + (3(x+2))/((x+2)(x-2))

Simplifying the numerators, we have:

(4x-8)/((x+2)(x-2)) + (3x+6)/((x+2)(x-2))

Combining the fractions, we get:

(4x-8+3x+6)/((x+2)(x-2))

Simplifying the numerator, we have:

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

Therefore, 4/(x+2)+3/(x-2) can be written as (7x-2)/((x+2)(x-2)) in its simplest form.

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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.