Intermediate Algebra

[faith21]

okay i dont even know where to start with this one:

r is not equal to +-2
r^2-5r+6 over r^2-4

i know this is terribly wrong but i have to show my process:
+-2^2-5 * +-2+6 over
+-2-4
=+-4-5 * +-2+6 over 2
=-1 * 8 over 2
=8 over 2

as you can see i dont know what am doin, and i certainly dont understand the +- so i made the 2 +- if it was going against a number to was bigger then it. it would be positive or negitive.

ex +-2 - 6= -4 cuz 6 is greater then 2 so 2 automaticly became negetive. am sorry for my ignorance plz help me

 

[Loren]

r is not equal to +-2
r^2-5r+6 over r^2-4

The first thing you need to do is find out what the directions are. You seem to be given a fraction...
\(\displaystyle \frac{r^2-5r+6}{r^2-4}\)

Of course r cannot be either a +2 or a -2 because if it were the denominator of this fraction would be zero which would imply division by zero which is not allowed. What are the instructions for this exercise? You might try factoring both the numerator and denominator and see if that suggests anything.

 

[mmm4444bot]

I guess that the instruction is to simplify this algebraic fraction?

(r^2 - 5r + 6)/(r^2 - 4)

The given line that reads, "r not equal to plus or minus two", is provided only as a confirmation that the denominator is not zero.

In other words, substituting 2 or -2 into the expression r^2 - 4 results in 4 - 4. We cannot divide by zero, so r cannot be either 2 or -2.

The given statement that r does not equal 2 or -2 is NOT used to simplify; it's just added information.

The key to simplifying the alebraic fraction is FACTORING!

Factor the polynomial in the numerator.

Do the same with the polynomial in the denominator.

Then you will see a common factor that cancels.

Do you know?

r^2 - 4 is called a Difference of Squares because 4 can be written as 2^2.

r^2 - 2^2

There is a special factoring pattern for differences of squares that you should memorize. Can you find it in your textbook?

Can you factor the numerator, too?

r^2 - 5r + 6 = (r + a)(r + b)

This is just like your previous post. You need to find the two numbers a and b by reasoning from the following facts.

a * b = 6

a + b = -5