# Math Help - Can a non-proportion equation be changed into a proportion? Class

1. ## 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?

2. Im' not sure exactly what you mean but if you multiply both sides of the equation through by $x(x-1)$ you get

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

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

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

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

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

3. Bit of an arithmetic error in the above answer, due to a sign problem...

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

whence

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

Happens to the best of us, at least twice a day.

4. Opps!

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

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

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

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

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