How do you combine #(4a-2)/(3a+12)-(a-2)/(a+4)#?

Answer 1

This equals #1/3#, with restriction #a != -4#

We can factor the denominator of the left-most expression as #3(a + 4)#, thus we multiply the second fraction by #3#.
#=(4a - 2 - 3(a - 2))/(3a + 12)#
#=(4a - 2 - 3a + 6)/(3a + 12)#
#=(a + 4)/(3a + 12)#
#=(a + 4)/(3(a + 4))#
#=1/3#
But don't forget that #a != -4#.

Hopefully this helps!

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Answer 2

See a solution process below:

To subtract or add fractions they must be over a common denominator. We can multiply the fraction on the right by the appropriate form of #1# to put these fractions over a common denominator:
#(4a - 2)/(3a + 12) - (3/3 xx (a - 2)/(a + 4)) =>#
#(4a - 2)/(3a + 12) - (3(a - 2))/(3(a + 4)) =>#
#(4a - 2)/(3a + 12) - (3a - 6)/(3a + 12)#

We can now subtract the numerators over the common denominator:

#((4a - 2) - (3a - 6))/(3a + 12) =>#
#(4a - 2 - 3a + 6)/(3a + 12) =>#
#(4a - 3a - 2 + 6)/(3a + 12) =>#
#((4 - 3)a + (-2 + 6))/(3a + 12) =>#
#(1a + 4)/(3a + 12) =>#
#(a + 4)/(3a + 12)#

We can now factor the numerator and cancel common terms:

#(a + 4)/(3(a + 4)) =>#
#color(red)(cancel(color(black)(a + 4)))/(3color(red)(cancel(color(black)((a + 4))))) =>#
#1/3#
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Answer 3

To combine the expressions (4a-2)/(3a+12) and (a-2)/(a+4), we need to find a common denominator. The common denominator for these expressions is (3a+12)(a+4).

Next, we multiply the first fraction (4a-2)/(3a+12) by (a+4)/(a+4), and the second fraction (a-2)/(a+4) by (3a+12)/(3a+12).

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

The simplified expression is (2a+6)/(3a+12).

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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.

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.

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.

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.

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