6/a^2-7a+6 Give the equivalent numerator if the denominator is (a - 6) (a - 1) (a + 6).

Question

Mathematics

Ari Cameron

4 June, 12:46

6/a^2-7a+6 Give the equivalent numerator if the denominator is (a - 6) (a - 1) (a + 6).

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Kyan Carrillo · Answer 1

1. The denominator for the first one factors out to (x+2) (x+2). You get this by taking the coefficient of "4" and finding mult's that if adding together would give you the middle x term which is + 4, then you would have x^2+2x+2x+4, you would use factor by grouping, (x^2+2x) (2x+4). Pull out the x from the first group, than a 2 from the second group. This will leave you with (x+2) (x+2). Now, the second part is "perfect squares," it is simply (2-x) (2+x). Now, with both of those done you come up with the final answer: (x+2) (2-x) is you LCD. If you are asking why not the (2+x), it is because that one is exact same as the (x+2), just written different but still the same value.

2. x/x^3+y^3, x/x+y: The first one is "perfect cubes" so it is the same as (x+y) ^3, which simply means (x+y) (x+y) (x+y). Your second fraction is (x+y), they are the same so your LCD is (x+y).

3. 6 / (a^2-7a+6) : First you must factor the denominator, just like problem #1 but the coeffienct is now a "+6" and you have to find mult's of 6 that add up to a "-7." I know that two negatives = positive. - 1*-6 give me my positive multiple and my - 7 when added together so the after factoring by grouping you get: (a-1) (a-6). Now that you have factored your denominator, you multiply both the top and bottom by the LCD that was given (x-2) (x-1) (x-6). The denominator (x-1) (x-6) is cancelled out by the same two LCD's and the only group that is left is (x-2). This is the only group that is left for you to mult the top with. So, now you only have 6 (a + 6) left, mult those through and get 6a+36, which is your final answer.

4. 2 / (x-2) : This one is simple, you just take the LCD given and mult it with (x-2). This leaves you with (x - 1) (x - 6) left and you mult these with the numerader for: 2 (x - 1) (x - 6). Make sure you mult through to get your final answer. You need to finish this one by mult'g 2 (x-1) (x-6), then you will have your final answer.

5. x-1 / (x^2-x-20) : Factor out the denominator like you did on the first examples then you should come up with (x-5) (x+4) for your denominator. Then mult it with the LCD (x - 5) (x + 4) (x + 3). The (x - 5) (x + 4) reduce to 1, there like before they are no longer there so all you have left is (x+3) to mult with the numerator and come up with your final answer.