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#.