$\displaystyle \frac {x^2-5x-6}{x -1} = x - 4 - \frac {10}{x -1}$
How to I achieve this simplification? So far I have:
$\displaystyle \frac {(x-6)(x+1)}{x -1}$
Am I on the right lines here?
Hello, hymnseeker!
One way is long division . . .$\displaystyle \frac {x^2-5x-6}{x -1} \;=\; x - 4 - \frac {10}{x -1}$
How to I achieve this simplification?
. . $\displaystyle \begin{array}{ccccc}
& & & x & - 4 \\
& & -- & -- & -- \\
x-1 & ) & x^2 & -5x & -6 \\
& & x^2 & -x \\
& & -- & -- \\
& & & -4x & -6 \\
& & & -4x & +4 \\
& & & -- & -- \\
& & & & -10
\end{array}$
Therefore: .$\displaystyle \frac{x^2-5x - 6}{x-1} \;=\;x - 4 - \frac{10}{x-1} $
Hi hymnseeker,
Another way is synthetic division. A very similar example is found at that link.
Solution: $\displaystyle x-4-\frac{10}{x-1}$Code:______________ 1 | 1 -5 -6 1 -4 ---------------- 1 -4 -10