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How do you combine #(2a + 1)/(3a+2) - (a-4)/(2-3a)#?

Answer 1

Eli Assouline

# (2a +1) /(3a +2) - (a-4)/(2-3a)#

cross multiplying for a common denominator : # ((2a +1) xx (2 - 3a) - (a-4) xx (3a +2))/((3a +2)(2-3a))#

# (4a - 6a^2 + 2 - 3a - (3a^2 + 2a - 12a - 8)) / ((cancel6a - 9a^2 +4 - cancel6a))#

#= (- 6a^2 - 3a^2 +4a - 3a -2a + 12a +2 + 8) / (- 9a^2 +4 )# #= (- 9a^2 + 11a + 10) / (- 9a^2 +4 )#

#= (9a^2 - 11a - 10) / ( 9a^2 - 4 )#

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Answer 2

Avery Alexander

To combine the expressions (2a + 1)/(3a+2) - (a-4)/(2-3a), we need to find a common denominator. The common denominator for these expressions is (3a+2)(2-3a).

Next, we can multiply the first fraction by (2-3a)/(2-3a) and the second fraction by (3a+2)/(3a+2) to get a common denominator.

After multiplying, we can simplify the numerators and combine the fractions by subtracting the second fraction from the first.

The simplified expression is: (2a + 1)(2-3a)/(3a+2)(2-3a) - (a-4)(3a+2)/(3a+2)(2-3a).

Further simplification may be possible depending on the specific values of 'a'.

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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.