SOLUTION: 2/x + 9 + 5/x + 2 = 3/x2 + 11x + 18

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Question 314575: 2/x + 9 + 5/x + 2 = 3/x2 + 11x + 18
Found 2 solutions by Fombitz, rapaljer:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean like this? Remember parentheses are a big help to remove any ambiguity (and they're free).
2%2F%28x+%2B+9%29+%2B+5%2F%28x+%2B+2%29+=+3%2F%28x%5E2+%2B+11x+%2B+18%29
2%2F%28x+%2B+9%29+%2B+5%2F%28x+%2B+2%29+=+3%2F%28%28x%2B2%29%28x%2B9%29%29
Multiply both sides by %28x%2B2%29%28x%2B9%29
2%28x%2B2%29%2B5%28x%2B9%29=3
2x%2B4%2B5x%2B45=3
7x%2B49=3
7x=-46
highlight_green%28x=-46%2F7%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28x+%2B+9%29+%2B+5%2F%28x+%2B+2%29+=+3%2F%28x2+%2B+11x+%2B+18%29

Factor the denominator on the right side of the equation, and multiply both sides by the LCD which turns out to be (x+9)(x+2).

2%2F%28x+%2B+9%29+%2B+5%2F%28x+%2B+2%29+=+3%2F%28%28x%2B9%29%28x%2B2%29%29
2%2F%28x+%2B+9%29+%2B+5%2F%28x+%2B+2%29+=+3%2F%28%28x%2B9%29%28x%2B2%29%29


Divide out the appropriate factors, and you are left with this:
2%28x%2B2%29+%2B+5%28x%2B9%29+=+3
2x%2B4%2B5x%2B45=3
7x+%2B+49=3
7x=+-46
x=-46%2F7
I know this is an ugly answer, but I don't see any errors to correct. Usually they come out better than this, but sometimes life doesn't comes out even.

For additional help with these topics, please see my OWN website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on my website which is given there, and look on my Homepage for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Intermediate Algebra", and look in "Chapter 2" for "2.07 Fractional Equation" where many of the exercises are solved IN COLOR on the "Math in Living Color" pages that go with this section.

Also, I have a video that was made a few years ago in one of my classes, that can be viewed from my website FREE. To see the videos look on my Homepage for the link "Rapalje Videos in Living Color." Choose "Intermediate Algebra", and look for the video "Fractional and Literal Equations". Let me know if they help, or if you have questions--my Email address is at the bottom of each page of my website. Math is usually not as hard as it looks!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus