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

Oct 17, 2015

$x - 4$.

Explanation:

Find the roots of the numerator: since it is a quadratic formula $a {x}^{2} + b x + c$ with $a = 1$, you can use the sum and product formula: you can write your expression as ${x}^{2} - s x + p$, 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 ${x}_{0} {x}_{1} = 4$. These numbers are easily found to be $1$ and $4$.

So, we can write ${x}^{2} - s x + p = \left(x - {x}_{0}\right) \left(x - {x}_{1}\right)$, and thus

${x}^{2} - 5 x + 4 = \left(x - 1\right) \left(x - 4\right)$. Plugging this into the fraction gives

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