how to simplify the expression : (x^2 + 3x - 4) / (x - 1)?

You simply must factor the first expression.

(If you do not know how to factor you must research it, it is complex to explain via text but is pretty easy once you get the hang of it.)

It factors into:

(x+4) times (x-1)

So the new equation is (x+4)(x-1) / (x-1)

you can cancel both the (x-1)'s in the numerator (top) and the denominator (bottom). This is a basic rule of fractions.

After doing so, you will left with the simplified and final answer of:

(x+4)

factorise the numerator

x^2 +3x - 4 = (x-1)(x+4)

so simplified version is x+4 (if x not = 1)

Factor out the numerator:

(x + 4)(x - 1) / (x - 1)

Simplify:

= x + 4

(x^2 + 3x - 4)/(x - 1) =

(x + 4)(x - 1)/(x - 1) =

x + 4

(x^2 + 3x - 4) / (x - 1)

= (x + 4)(x - 1) / (x - 1)

= x + 4