Solve the following rational equation algebraically. x^2/2 = x/(x-1) Determine the point(s) of intersection of the following rational function... f(x)= (2x+3) / x Thanks.
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Originally Posted by johett Solve the following rational equation algebraically. x^2/2 = x/(x-1) Determine the point(s) of intersection of the following rational function... f(x)= (2x+3) / x Thanks. $\displaystyle \frac{x^2}{2} = \frac{x}{(x-1)}$ $\displaystyle (x-1)x^2 = 2x$ $\displaystyle x^3-x^2 - 2x = 0$ $\displaystyle x^2-x - 2 = 0$; Keep in mind x can equal zero! $\displaystyle (x+1)(x-2) = 0$ $\displaystyle x=-1,0,2$
Last edited by colby2152; Jan 2nd 2008 at 10:58 AM.
Originally Posted by colby2152 $\displaystyle x^3-x^2 - 2x = 0$ $\displaystyle x^2-x - 2 = 0$ Careful with this step. $\displaystyle x=0$ satisfies the original equation too.
Originally Posted by colby2152 $\displaystyle \frac{x^2}{2} = \frac{x}{(x-1)}$ $\displaystyle (x-1)x^2 = 2x$ $\displaystyle x^3-x^2 - 2x = 0$ $\displaystyle x^2-x - 2 = 0$ Iso: NO, NO!!If you carelessly divide you will miss x=0 solution!! $\displaystyle (x+1)(x-2) = 0$ $\displaystyle x=-1,2$ Apart from that everything else is perfect
Originally Posted by Krizalid Careful with this step. $\displaystyle x=0$ satisfies the original equation too. Yeah, the guys caught me going too fast. Even a seasoned vet will make mistakes if the work becomes too sloppy!
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