#43 is a problem in which you have to factor the top of the equation...then you can cancel out like terms.
x^2-x-2 can be factored into (x-2)(x+1) so you have x+1 in the numerator and the denominator so they can be cancelled leaving x-2.
Factoring works this way...you know you'll have (x)(x) because of the x^2 so write (x ?)(x ?)...Now what times what would give you a -2??? Either 2 * -1 or 1 * -2...so you know that one set of these numbers will fit into the second part of the parentheses...the clue is that with a (-x) in the middle of the equation you know what you use a -2 because -2 + 1 = -1...or since you're adding -2x + (1)x = -x.
(x-2)(x+1)...To check your work, work backwards by multiplying the terms in this manner (First, Oustside, Inside, Last) or known as the FOIL method...
So x*x, x*1, -2*x, -2*1...the answer is x^2+1x-2x-2 or simplying the x's as x^2 - x - 2. You have the original equation...
Here's a little harder one I've made up...2x^2 - 2x - 12 / (x + 2)
The trick to factoring the numerator here is to factor out any whole number multiple first...or 2 in this case...So 2(x^2 - x - 6) / (x + 2)
Now factor as before 2(x ?)(x ?)/ (x+2)...factors of -6 are: -1,6; -6,1; 2,-3; -3,2...which two will leave you a -1x when added to together?...(-3,2)
So 2 (x-3)(x+2) / (x+2)....cancel the (x+2)'s leaving an Answer of
2(x-3).
The main trick to figuring out a simplified math test such as the ASTB is to understand that almost always the denominator will be one of the factors in the numerator allowing for cancelling...Knowing this will help save a few second in solving.
Hope that helps.