SOLUTION: How would you figure out this question? 2x+3 - 3 = 2 ____ _ x-1 x I don't know how to write that better... How would you work this out? This is what I attempted: x(2

Question 232497: How would you figure out this question?
2x+3 - 3 = 2
____ _
x-1 x
I don't know how to write that better...
How would you work this out? This is what I attempted:
x(2x+3) - 3x+3 = 2x^2-2x
______________
x^2-x
What do you do from there or am I wrong?
Thanks,
BrownieGirl7

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This is an EQUATION, and what you did was multiply both sides by the common denominator. In these problems in the second step, there is NO denominator (since you MULTIPLIED each fraction times the LCD, the denominator factors divide out in each fraction!). This is what I call the "Fraction Haters' Delight!" since there are NO denominators left in the whole problem after the second step!!

Now you just have to solve this equation, which you already had:

x(2x+3) - 3x+3 = 2x^2-2x
2x^2 +3x -3x+3 = 2x^2 -2x

Subtract 2x^2 from each side, and all the x^2 terms subtract out:
3=-2x

Divide both sides by -2: x= -3/2

Now you have to check each denominator to make sure NO denominators equal zero. In this case, they do not equal zero if x=-3/2, so the answer is acceptable.

For additional help with this topic, please visit my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. From my Homepage, look for "MATH IN LIVING COLOR." Select "Basic Algebra" and look in "Chapter 2" for "Section 2.07 Fractional Equations." The problems there are solved with detailed explanations IN LIVING COLOR. My explanations were written FOR and TO students, a LOT easier to understand than traditional textbooks.

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

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