First things first you need to factor the denominator of each expression. The first denominator can be factored into (x+1)*(X+3) and the second denominator can be factored into (x-3)*(x+3).
Next you need to create a common denominator, as you see (X+3) is common to both, so you common denominator will be (x+3)(x-3)(x+1) - hint it's easiest to take X^2 -9 and just multiply it by (x+1) - this will be your common denominator - you can figure out that answer.
Lastly, you just need to multiply your numerator but what you multiplied the denominator by (the property of multiplying by one) so all you need to do is multiply 3 times (x-3) and multiply 1 times (X+1).
Then you can combine the numerators and you have your answer.
Answers & Comments
Verified answer
3 / (x^2 + 4x + 3) - 1 (x^2 - 9)
Step 1: Factor the terms.
x^2 + 4x + 3 factors out as (x + 3) (x + 1)
x^2 - 9 factors out as (x + 3) (x - 3)
Step 2: Create a common denominator:
3 / ((x + 3) (x + 1)) * (x - 3) / (x - 3) =
3 (x - 3)/ ((x + 3) (x + 1) (x - 3))
1 / ((x + 3) (x - 3)) * (x + 1) / (x + 1) =
1 (x + 1) / ((x + 3) (x + 1) (x - 3))
Step 3: Subtract the common fractions:
(3 (x - 3) - 1(x + 1)) / ((x + 3) (x + 1) (x - 3))
(3x - 9 - x - 1) / ((x + 3) (x + 1) (x - 3))
(2x -10) / ((x + 3) (x + 1) (x - 3)) (solution)
or: 2 (x - 5) / (x^3 + x^2 - 9x - 9) (solution)
First things first you need to factor the denominator of each expression. The first denominator can be factored into (x+1)*(X+3) and the second denominator can be factored into (x-3)*(x+3).
Next you need to create a common denominator, as you see (X+3) is common to both, so you common denominator will be (x+3)(x-3)(x+1) - hint it's easiest to take X^2 -9 and just multiply it by (x+1) - this will be your common denominator - you can figure out that answer.
Lastly, you just need to multiply your numerator but what you multiplied the denominator by (the property of multiplying by one) so all you need to do is multiply 3 times (x-3) and multiply 1 times (X+1).
Then you can combine the numerators and you have your answer.
2(x-5) / (x+3)(x-3)(x+1)
factorize the denominator of the first fraction
3/(x+1)(x+3) - 1/(x+3)(x-3)
= [3(x-3)-(x+1)]/[(x+1)(x-3)(x+3)]
= (2x-10)/ (x^3+x^2-9x-9)
factor the bottom first..... then find the common denominator......multiply it by the tops and then subtract....
(x+3)(x+1) and (x+3)(x-3) factored
3*(x-3) and 1*(x+1) multiply
now subtract
that equation comes to:
3/ (x+3)(x+1) - 1/(x+3)(x-3)
make into common denominator of (x+3)(x+1)(x-3)
3(x-3) / (x+3)(x-3)(x+1) - 1(x+1) / (x+3)(x-3)(x+1)
3x-9/(x+3)(x-3)(x+1) - x+1/(x+3)(x-3)(x+1)
2x-10 / (x+3)(x-3)(x+1)
2x-10 / (x^2-9)(x+1)
Ooookay 2+2=3 Ha! only if my math teacher Mr. Friedman can see me know.
yes or maybe true? math was never my good subject. on second thought 'c' is the correct answer!!