need help w/ simplifying (r^2-5r+y)/(r^2-4), translating

[muddigger]

I am getting ready to go to college and I have been out of school for 6 years now and I have to take a placement test and these questions are on the sample test question and I have forgotten how to do them so any help would be great.
4.For all r is not equal to plus or minus 2, (r squared - 5r + 6) over (r squared - 4) = ?
A. (r - 3) over (r + 2)
B. (r - 2) over (r + 2)
C. (r - 2) over (r + 3)
D. (r + 3) over (r - 2)
E. (r + 3) over (r + 2)

2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. –6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 – 5x + 6
D. 6x2 – 5x – 6
E. 6x2 – 13x – 6

if you could please so me step by step and give me notes to help me remember how to do them

 

[Loren]

Re: going back to school and need all the help I can get

For all r is not equal to plus or minus 2, (r squared - 5r + 6) over (r squared - 4) = ?
\(\displaystyle \frac{r^2-5r+6}{r^2-4}\)

Factor both numerator and denominator. You will see a common factor in each. Remember that any quantity divided by itself (except zero) = 1. Some would tell you to "cancel".

the product of 3 less than twice x and 2 more than the quantity 3 times x ?

Product means that two or more things are multiplied together. One of those things is the quantity that is 3 less than 2 times x. In other words multiply 2 times x and then subtract 3. The other thing is 2 more than "3 times x".
Maybe you can put it all together now???

 

[stapel]

if you could please so me step by step and give me notes to help me remember how to do them

Since we cannot provide the requested classroom instruction within this environment, please consider studying from some online lessons instead. :idea:

Note: Neither of these exercises is from "pre-algebra". For "hard copy" lessons, you'll want to get a text on algebra.

For the first exercise, you need to learn how to factor, then how to factor quadratics (also referred to as "trinomials", in certain cases), and then how to do some special factoring.

. . . . .Google results for "simple factoring"

. . . . .Google results for "factoring quadratics"

. . . . .Google results for "factoring trinomials"

. . . . .Google results for "special factoring squares cubes"

To learn how to "translate" English into math, try here:

. . . . .Google results for "translate word problem"

Have fun!

Eliz.