Rational equations algebraically (quick question)

**johett** · January 2nd 2008, 08:47 AM

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.

**colby2152** · January 2nd 2008, 09:26 AM

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.

$\frac{x^2}{2} = \frac{x}{(x-1)}$

$(x-1)x^2 = 2x$

$x^3-x^2 - 2x = 0$

$x^2-x - 2 = 0$ ; Keep in mind x can equal zero!

$(x+1)(x-2) = 0$

$x=-1,0,2$

**Krizalid** · January 2nd 2008, 10:14 AM

Originally Posted by colby2152

$x^3-x^2 - 2x = 0$

$x^2-x - 2 = 0$

Careful with this step.

$x=0$ satisfies the original equation too.

**Isomorphism** · January 2nd 2008, 10:14 AM

Originally Posted by colby2152

$\frac{x^2}{2} = \frac{x}{(x-1)}$

$(x-1)x^2 = 2x$

$x^3-x^2 - 2x = 0$

$x^2-x - 2 = 0$
Iso: NO, NO!!If you carelessly divide you will miss x=0 solution!!

$(x+1)(x-2) = 0$

$x=-1,2$

Apart from that everything else is perfect

**colby2152** · January 2nd 2008, 10:23 AM

Originally Posted by Krizalid

Careful with this step.

$x=0$ 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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