1981 AHSME Problems/Problem 6
Revision as of 15:55, 28 January 2021 by Coolmath34 (talk | contribs) (Created page with "==Problem== If <math>\frac{x}{x-1} = \frac{y^2 + 2y - 1}{y^2 + 2y - 2},</math> then <math>x</math> equals <math>\text{(A)} \quad y^2 + 2y - 1</math> <math>\text{(B)} \quad y...")
Problem
If 
then 
equals
Solution
We can cross multiply both sides of the equation and simplify.
![\[x(y^2 + 2y - 2) = (x-1)(y^2 + 2y - 1)\]](http://latex.artofproblemsolving.com/a/6/a/a6ade39e0e30d561d34f1f7a0424ed8739d21096.png)
![\[xy^2 + 2xy - 2x = xy^2 + 2xy - x - y^2 - 2y + 1\]](http://latex.artofproblemsolving.com/1/b/1/1b18b6e7b030feff8a95e7a5c02757e52089beab.png)
![\[-x = -y^2 - 2y + 1\]](http://latex.artofproblemsolving.com/5/3/7/5373f3f1b1cd03df689803c0bacc077d10c8bac5.png)
![\[x = y^2 + 2y - 1\]](http://latex.artofproblemsolving.com/6/9/3/693f25182ec1ff5724d70fe8c231898895706590.png)
The answer is 
-edited by coolmath34
