1963 TMTA High School Algebra I Contest Problem 31
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Problem
Solve for 
when 
Solution
Simplify.
![\[\frac{x}{x-1} = \frac{3(x-1)+1}{x-1}=\frac{3x-2}{x-1}\]](http://latex.artofproblemsolving.com/6/b/d/6bd52e72503c1c32c3e4e45a644c24b1de64f6a6.png)
Cross multiply.
![\[(x)(x-1)=(3x-2)(x-1)\]](http://latex.artofproblemsolving.com/b/1/b/b1be57abb4e0295e691e2b0a7fc656417004392b.png)
![\[x^2 - x = 3x^2 - 5x + 2\]](http://latex.artofproblemsolving.com/7/a/1/7a1ccb7064dce64e15d38a8f05bcc704985447bc.png)
![\[0 = 2x^2 - 4x + 2\]](http://latex.artofproblemsolving.com/2/6/0/260982397c7dd736b4bdd8765881f326d138c989.png)
This yields 
as a solution, but this is extraneous since ![\[1-1=0\]](http://latex.artofproblemsolving.com/6/6/1/66118bb819416866907439da6d5123d93e062797.png)
, and the denominator in the fractions given cannot be ![\[0\]](http://latex.artofproblemsolving.com/5/b/f/5bfabc1cb10da61af0146af2ab7b7f3a783239a6.png)
, so the answer is 
See Also
| 1963 TMTA High School Mathematics Contests (Problems) | ||
| Preceded by Problem 30 |
TMTA High School Mathematics Contest Past Problems/Solutions | Followed by Problem 32 |
