With a fraction don’t be so quick to multiply. Usually it makes sense to cut down to smaller numbers first. You should be in the habit to factor and cancel with fractions!!!

Here is an example when simplifying. Many students jump straight into multiplication.

  \huge \frac{2(x+3)(x -4)}{3x + 2 – 3x}  \\ = \\ \frac{2x^2 – 2x -24}{3x + 2 – 3x} 

But now what? You would have to simplify the bottom and and the look to factor. Why multiply if you only have to factor again?

Better to simplify the bottom and see what happens next!

  \huge \frac{2(x+3)(x -4)}{3x + 2 – 3x}  = \frac{2(x+3)(x -4)}{ 2 } =  (x+3)(x -4)

The key here was to wait until you simplified. It is usually a good idea to keep algebraic fractions in factored form unless you have a good reason not to.