# Thread: Rational equations algebraically (quick question)

1. ## Rational equations algebraically (quick question)

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.

2. 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!

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

$\displaystyle x=-1,0,2$

3. 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.

4. 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

5. 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!