Intermediate Algebra: Rational Expessions?

Question

r ^2 - 5r + 6
_________ =

r ^2 - 4 Could you please break this down to me

Answer 1

The numerator, r ^2 - 5r + 6, would need to be factored out. Find 2 numbers with a difference (subtraction sign) of 5 and a product of 6. These numbers are 2 and 3.

(r - 2)(r - 3) = numerator

Now for the denominator:

The factors of r^2 - 4 are conjugates. (r - 2)(r + 2)

(r - 2)(r - 3)
--------------
(r - 2)(r + 2)

The (r-2) cancel each other out so your final answer is:

(r - 3)
--------
(r + 2)

Answer 2

1. r ^2 - 5r + 6

you can use a big “X” method. Write down a big X on paper.
Multiply the first and last coefficient: (1)(6) = 6 and write it on the top of the X.
Write the middle coefficient (-5) on the bottom of the X.

Find two numbers that give you 6 when multiplied together and give you –5 when added or subtracted from one another.

Two numbers: -3, -2 because (-3)(-2) = 6 and –3 –2 = -5

Rewrite as (x – 3) (x – 2)

2. r ^2 – 4
first, break each set apart:

r^2 is (r)(r)

and – 4 is (–2)(2)

(r - 2)(r + 2)

one is negative and one is positive to give you – 4

Answer 3

Not sure which step you need the help with.

You need to factor each expression to have any hope of simplifying. As long as there are + or - signs in either the numerator or denominator, it is extremely difficult to simplify.

Or do you not know how to factor? Find two numbers x and y such that x + y is the middle multiplier in the trinomial and that x * y is the 3rd. Then the factors are (r + x)(r + y). Either that, or use the quadratic formula. The formula is a bit complex but it works when simple trial and error in the first way don't get you the answer.

Or do you not know how the simplify? Once you have (r-2)(r-3) on the top and (r-2)(r+2) on the bottom, you can remove (r-2) from both leaving (r-3)/(r+2)

Answer 4

(r-3)(r-2) honey you should get parantizez and i mean you should first write the x in the parantez then you should find two numbers which the sum of them is 5 (the number with not too much power and not with power 1 )and the number with power one is the nimber that you should find two numbers which when you multiply them you should get that number. sorry my english is not good so you may not understand whaT I MEAN. AND ABOUT THE SECOND one:(r-2)(r+2). good bye little girl!

Answer 5

find what multiplies to equal 6 (outside number) and adds together to equal 5 (middle number)
so you get (r-3)and (r-2)
-2x-3=6 and -2+-3= 5
the final answer is the opposite of whats in the ()= 3 & 2

the second one is something that multiplies to 4 and adds to 0
so (r-2) & (r+2)
final answer is opposite of () or 2,-2

Answer 6

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Answer 7

(r^2-5r+6)/(r^2-4)
(r-3)(r-2)/((r+2)(r-2))
(r-3)/(r+2)