Answer:
Step-by-step explanation:
Lots of factoring here. Let's rewrite everything in its simplest, factored form:
[tex]\frac{\frac{(x-1)(x+3)}{(x-4)} }{\frac{(2x-1)(x+3)}{(x+4)(x-4)} }[/tex]
The term (x - 4) cancels out completely, leaving us with
[tex]\frac{(x-1)(x+3)}{\frac{(2x-1)(x+3)}{(x+4)} }[/tex]
Let's get rid of that (x + 4) by multiplying both top and bottom by (x + 4) to get
[tex]\frac{(x-1)(x+3)(x+4)}{(2x-1)(x+3)}[/tex]
It's obvious now that the (x + 3) term cancels out, leaving us with
[tex]\frac{(x-1)(x+4)}{(2x-1)}[/tex]
Now all that's left to do is to FOIL out the numerator:
[tex]\frac{x^2+3x-4}{2x-1}[/tex]
The first choice is the one you want
