How do you simplify (x^2-5x+4) /(x-1)?

1 Answer
Oct 17, 2015

x-4.

Explanation:

Find the roots of the numerator: since it is a quadratic formula ax^2+bx+c with a=1, you can use the sum and product formula: you can write your expression as x^2-sx+p, where s is the sum of the roots, and p is their product. So, we're looking for two numbers x_0 and x_1 such that x_0+x_1=5, and x_0x_1=4. These numbers are easily found to be 1 and 4.

So, we can write x^2-sx+p=(x-x_0)(x-x_1), and thus

x^2-5x+4 = (x-1)(x-4). Plugging this into the fraction gives

{cancel((x-1))(x-4)}/{cancel(x-1), and the expression simplifies into x-4.