1. Simplifying algebraic fraction

$\displaystyle \frac {x^2-5x-6}{x -1} = x - 4 - \frac {10}{x -1}$

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?

2. Hello, hymnseeker!

$\displaystyle \frac {x^2-5x-6}{x -1} \;=\; x - 4 - \frac {10}{x -1}$

How to I achieve this simplification?
One way is long division . . .

. . $\displaystyle \begin{array}{ccccc} & & & x & - 4 \\ & & -- & -- & -- \\ x-1 & ) & x^2 & -5x & -6 \\ & & x^2 & -x \\ & & -- & -- \\ & & & -4x & -6 \\ & & & -4x & +4 \\ & & & -- & -- \\ & & & & -10 \end{array}$

Therefore: .$\displaystyle \frac{x^2-5x - 6}{x-1} \;=\;x - 4 - \frac{10}{x-1}$

3. That works, thank you Soroban.

4. Originally Posted by hymnseeker
$\displaystyle \frac {x^2-5x-6}{x -1} = x - 4 - \frac {10}{x -1}$

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?
Hi hymnseeker,

Another way is synthetic division. A very similar example is found at that link.

Code:
   ______________
1 | 1  -5  -6
1  -4
----------------
1  -4  -10
Solution: $\displaystyle x-4-\frac{10}{x-1}$