<h3>Answer: Choice B</h3>
which is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))
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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.
turns into
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So,
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.