i am lost with problems like these, can someone please help and explain step by step?
Factorise both the numerator and denominator.
Numerator:
$\displaystyle 2x^2-x-3 $
That can be factorised to: $\displaystyle (x+1)(2x-3) $
Denominator:
$\displaystyle x-1 $
That can be factorised to: $\displaystyle (x+1)(x-1) $
Now we have a fraction that looks like this:
$\displaystyle \frac{(x+1)(2x-3)}{(x+1)(x-1)} $
Now have a think of what you do next....
No, it can't! You were thinking of $\displaystyle x^2- 1$.
That should be $\displaystyle \frac{(x+1)(2x-3)}{x-1}$Now we have a fraction that looks like this:
$\displaystyle \frac{(x+1)(2x-3)}{(x+1)(x-1)} $
Now have a think of what you do next....
By the way, wonderd, you never did say what you wanted to do with that expression!
You're probably expected to do a polynomial long division to get the result here: simplify (2x^2 - x - 3)/(x - 1) - Wolfram|Alpha
Your textbook and class notes should have examples ....?