Simplify 3(x-5)/x^2-3x-10

The question is asking us to simplify; in particular, we have to simplify a fraction. We simplify a fraction by cancelling a factor from both the numerator and the denominator. We can apply this algebraically through factorisation. In our example, we see that the numerator is already factorised so we may leave this. The denominator is a quadratic expression, we may factorise by finding out what multiplies to make our last term (-10) and adds to make our x term (-3). By computation we find this to be -5 and +2. Our factorised form for the denominator is therefore given by:

 x^2-3x-10 = (x-5)(x+2). Combining our results, we find a common factor of (x-5), thus we can cancel (x-5) giving us the simplification: 3(x-5)/x^2-3x-10=3/(x-2)