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How do you add #(x^2+2x)/(12x+54) - (3-x)/(8x+36)#?

Answer 1

Julia Adams

Factorize

#=(x^2+2x)/(6(2x+9))-(3-x)/(4(2x+9))# #=1/(2(2x+9))*{(x^2+2x)/3-(3-x)/2}#

#=1/(4x+18)*{(2(x^2+2x)-3(3-x))/6}#

#=1/(4x+18)*{(2x^2+4x-9+9x)/6}#

#=1/(4x+18)*{(2x^2+13x-9)/6}# #=(2x^2+13x-9)/(24x+108)#

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Answer 2

Abigail Allen

To add the given expressions, we need to find a common denominator for both fractions. The common denominator is (12x + 54)(8x + 36).

Next, we multiply the numerator and denominator of the first fraction, (x^2 + 2x), by (8x + 36), and the numerator and denominator of the second fraction, (3 - x), by (12x + 54).

Expanding these expressions, we get (8x^3 + 36x^2 + 16x^2 + 72x) / (12x + 54)(8x + 36) - (36x + 162 - 12x^2 - 54x) / (12x + 54)(8x + 36).

Simplifying the numerators, we have (8x^3 + 52x^2 + 72x) / (12x + 54)(8x + 36) - (12x^2 - 18x + 162) / (12x + 54)(8x + 36).

Combining the fractions, we get (8x^3 + 52x^2 + 72x - 12x^2 + 18x - 162) / (12x + 54)(8x + 36).

Simplifying the numerator further, we have (8x^3 + 40x^2 + 90x - 162) / (12x + 54)(8x + 36).

Therefore, the simplified expression is (8x^3 + 40x^2 + 90x - 162) / (12x + 54)(8x + 36).

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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.