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How do you combine #1/3 + 7/(3x) - 2/(3x+6) #?

Answer 1

Genesis Allen

Note #color(red)(3)(x^2+2x) = color(blue)(3x)(x+2)= color(green)((3x+6)(x)#

So #1/color(red)(3) + 7/(color(blue)(3x)) - 2/(color(green)(3x+6))#

#= (3(x^2+2x) +7(x+2)-2(x)) / ( 3x^2+6x)#

#= (3x^2+11x+14)/(3x^2+6x)#

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Answer 2

Nathan Axel

#=1/3(1+7/x-2/(x+2))=1/3(7/x+1-2/(x+2))#

#=1/3(7/x+x/(x+2))#

#=1/3((7(x+2)+x^2)/(x(x+2)))#

#=1/3((7x+14+x^2)/(x(x+2)))#

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Answer 3

Eva Adamson

To combine the given expressions, we need to find a common denominator. The common denominator for 1/3, 7/(3x), and 2/(3x+6) is 3x(3x+6).

Multiplying 1/3 by (3x+6)/(3x+6), we get (3x+6)/(9x+18).

Multiplying 7/(3x) by (3)/(3), we get 21/(9x).

Multiplying 2/(3x+6) by (3)/(3), we get 6/(9x+18).

Now, we can combine the fractions: (3x+6)/(9x+18) + 21/(9x) - 6/(9x+18).

Combining the numerators over the common denominator, we have (3x+6 + 21 - 6)/(9x+18).

Simplifying the numerator, we get (3x+21)/(9x+18).

Further simplifying, we can divide both the numerator and denominator by 3: (x+7)/(3x+6).

Therefore, the combined expression is (x+7)/(3x+6).

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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.