SOLUTION: Found this on an SAT Practice test. (6x-1)/(x+4) Which of the following is equivalent to the expression above? A) 6-[25/(x+4)] B) 6-[1/(x+4)] C) 6-(1/4) D) (6-1)/4 H

Algebra ->  Expressions-with-variables -> SOLUTION: Found this on an SAT Practice test. (6x-1)/(x+4) Which of the following is equivalent to the expression above? A) 6-[25/(x+4)] B) 6-[1/(x+4)] C) 6-(1/4) D) (6-1)/4 H      Log On


   

Question 1122263: Found this on an SAT Practice test.
(6x-1)/(x+4)
Which of the following is equivalent to the expression above?
A) 6-[25/(x+4)]
B) 6-[1/(x+4)]
C) 6-(1/4)
D) (6-1)/4
Hopefully the parentheses I added make it less confusing.
So, I know it's not C or D, since, well, where did the x go? So, that leaves A and B. I looked at the answers and found that it is A, but why? How can I get from (6x-1)/(x+4) to 6-[25/(x+4)]? Please show steps, I need to learn this so I can get this right in the future.
Found 4 solutions by josgarithmetic, greenestamps, solver91311, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Found this on an SAT Practice test.
(6x-1)/(x+4)
Which of the following is equivalent to the expression above?
---------------------------------------------

Is it choice B?

6-1%2F%28x%2B4%29

6%28x%2B4%29%2F%28x%2B4%29-1%2F%28x%2B4%29

%286x%2B24-1%29%2F%28x%2B4%29

%286x%2B23%29%2F%28x%2B4%29
Not apparently.


Is it choice A?
6-25%2F%28x%2B4%29
6%28x%2B4%29%2F%28x%2B4%29-25%2F%28x%2B4%29
%286x%2B24-25%29%2F%28x%2B4%29
%286x-1%29%2F%28x%2B4%29
Yes, seems to be.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here's the way I think of this kind of problem. Perhaps (I hope) you will get responses from other tutors showing you the way they work problems like this -- in case my method doesn't "work" for you.

(1) In the numerator I have "6x"; in the denominator I have just "x". That means the whole number part of my answer is going to be 6. (and you can see that in the answer choices).

(2) So make a fraction with denominator (x+4) that is equivalent to the whole number 6:

6+=+%286%28x%2B4%29%29%2F%28x%2B4%29+=+%286x%2B24%29%2F%28x%2B4%29

(3) Now, how does the numerator of that fraction compare to the denominator of the given fraction? I have 6x+24 and I want 6x-1.

%286x%2B24%29-25+=+%286x-1%29

(4) So

Answer A.

Answer by solver91311(24713) About Me  (Show Source):
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There are a couple of ways to get there. The straight-up way is to simply do polynomial long division on the original rational expression: 

            6 
      ________
x + 4 )6x -  1
       6x + 24  {remember, change the sign and add}
       _______
          - 25


So goes into 6 times with a remainder of -25. Or, as answer A puts it:



Or you could just get clever and notice that -1 can be written as 24 - 25:




John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Found this on an SAT Practice test.
(6x-1)/(x+4)
Which of the following is equivalent to the expression above?
A) 6-[25/(x+4)]
B) 6-[1/(x+4)]
C) 6-(1/4)
D) (6-1)/4
Hopefully the parentheses I added make it less confusing.
So, I know it's not C or D, since, well, where did the x go? So, that leaves A and B. I looked at the answers and found that it is A, but why? How can I get from (6x-1)/(x+4) to 6-[25/(x+4)]? Please show steps, I need to learn this so I can get this right in the future.
       6         
x + 4)6x -  1
      6x + 24
         - 25 (Remainder)

From above, you can see that the answer is: