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Darla found that the least common denominator needed to subtract \frac{x}{x^2+4x-12}-\frac{3}{x+6}is (x + 6)(x – 2). Which is the correct next step?

\frac{x−3}{x^2+3x−18}
x/(x+6)(x−2) – 3(x−2)/(x+6)(x−2)
x/(x+6)(x−2) – 3(x+6)/(x+6)(x−2)
x(x+6)(x−2)/(x+6)(x−2) – 3(x+6)(x−2)/(x+6)(x−2)

2 Answers

2 votes

Answer:

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

Step-by-step explanation:

User Michael Kunst
by
8.4k points
6 votes

Answer: Choice B


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

which is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

=====================================

Step-by-step explanation:

The LCD is (x+6)(x-2) which is the factorization of x^2+4x-12, and that is the denominator of the first fraction. The first fraction has the LCD already. The second fraction does not. It has (x+6) but it is missing (x-2).

We multiply top and bottom of the second fraction by (x-2) to get the second fraction to have the LCD.


(3)/(x+6) turns into
(3)/(x+6)*(x-2)/(x-2) = (3(x-2))/((x+6)(x-2))

------

So,


(x)/(x^2+4x-12) - (3)/(x+6)


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


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

This is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

Note the parenthesis around "(x+6)(x-2)"

Instead of x/(x+6)(x-2) you should write x/( (x+6)(x-2) ) to ensure that all of "(x+6)(x-2)" is in the denominator.

User Joseph Mansfield
by
8.0k points

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