How do you simplify (x^2-5x+4) /(x-1)x25x+4x1?

1 Answer
Oct 17, 2015

x-4x4.

Explanation:

Find the roots of the numerator: since it is a quadratic formula ax^2+bx+cax2+bx+c with a=1a=1, you can use the sum and product formula: you can write your expression as x^2-sx+px2sx+p, where ss is the sum of the roots, and pp is their product. So, we're looking for two numbers x_0x0 and x_1x1 such that x_0+x_1=5x0+x1=5, and x_0x_1=4x0x1=4. These numbers are easily found to be 11 and 44.

So, we can write x^2-sx+p=(x-x_0)(x-x_1)x2sx+p=(xx0)(xx1), and thus

x^2-5x+4 = (x-1)(x-4)x25x+4=(x1)(x4). Plugging this into the fraction gives

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