How would you change, for example, the equation
1/x + 3/(x-1) = 101
into proportion? Class?
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 $
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.