Can a non-proportion equation be changed into a proportion? Class

• Jul 6th 2009, 01:39 PM
domino2339
Can a non-proportion equation be changed into a proportion? Class
How would you change, for example, the equation

1/x + 3/(x-1) = 101

into proportion? Class?
• Jul 6th 2009, 02:06 PM
pickslides
Im' not sure exactly what you mean but if you multiply both sides of the equation through by $\displaystyle x(x-1)$ you get

$\displaystyle (x-1)-3x = 101 x(x-1)$ then this can be simplified as follows.

$\displaystyle -1-2x = 101 (x^2-x)$

$\displaystyle -1-2x = 101 x^2-101x$

$\displaystyle 0 = 101 x^2-99x+1$

$\displaystyle 101 x^2-99x+1= 0$
• Jul 6th 2009, 07:18 PM
AlephZero
Bit of an arithmetic error in the above answer, due to a sign problem...

Should be
$\displaystyle \frac{x-1+3x}{x(x-1)}=101$

whence

$\displaystyle 101x^2-105x+1=0$, then quadratic formula to solve for $\displaystyle x.$

Happens to the best of us, at least twice a day.
• Jul 6th 2009, 07:25 PM
pickslides
Opps!

$\displaystyle (x-1)+3x = 101 x(x-1)$ then this can be simplified as follows.

$\displaystyle -1+4x = 101 (x^2-x)$

$\displaystyle -1+4x = 101 x^2-101x$

$\displaystyle 0 = 101 x^2-105x+1$

$\displaystyle 101 x^2-105x+1= 0$