# How do you multiply (5x+2)/(3x)-(4x-3)/(3x)=( x-1 )/(3x)?

May 19, 2015

I am not sure if you want to solve it for $x$ but I try this:
Take a common denominator on both sides:
$\frac{5 x + 2 - 4 x + 3}{3 x} = \frac{x - 1}{3 x}$
Now take the $3 x$ from the denominator (on the left) up to multiply on the right as:
$5 x + 2 - 4 x + 3 = \left(x - 1\right) \frac{\textcolor{red}{3 x}}{3 x}$ and simplify:
$5 x + 2 - 4 x + 3 = \left(x - 1\right) \frac{\cancel{\textcolor{red}{3 x}}}{\cancel{\left(3 x\right)}}$
$x + 5 = x - 1$
$0 = - 6$ which in not true for any $x$