Homeschooling mom needs help!! Daughter is too smart for me!!!
(a^2-a-2)/(a^2-7a+10)-(a^2-2a-3)/(a^2+5a+4)
A)-3a-11/(a-5)(a+4)
B)13a-11/(a-5)(a+4)
C) -3a+19/(a-5)(a+4)
D)a^2-13a-11/(a-5)(a+4)
a^2-a-2 = (a-2)(a+1)
a^2-7a+10 = (a-2)(a-5)
So, the first fraction is just (a+1)/(a-5)
a^2-2a-3 = (a-3)(a+1)
a^2+5a+4 = (a+4)(a+1)
So, the 2nd fraction is just (a-3)/(a+4)
Now you have
(a+1)/(a-5) - (a-3)/(a+4)
putting it all over a common denominator of (a-5)(a+4), the numerator becomes
(a+1)(a+4) - (a-3)(a-5)
= a^2+5a+4 - (a^2-8a+15)
= a^2+5a+4-a^2+8a-15
= 13a-11
so (B) is the answer
Thank you Steve! She had the right answer, I was just checking my own thinking. I appreciate the help from all of you, it makes my life a little bit easier. I just wanted to let you know that.
aw, shucks. >scuff scuff<
we aim to please, ma'am.
To simplify the given expression, you can follow these steps:
1. Factorize the denominators of both fractions.
(a^2-7a+10) can be factored as (a-5)(a-2).
(a^2+5a+4) can be factored as (a+4)(a+1).
2. Find the least common denominator (LCD) by taking the product of the two denominators: (a-5)(a-2)(a+4)(a+1).
3. Perform the subtraction and combine the fractions into a single fraction over the LCD.
(a^2-a-2)/(a^2-7a+10) - (a^2-2a-3)/(a^2+5a+4) becomes:
[(a^2-a-2)(a+4)(a+1) - (a^2-2a-3)(a-5)(a-2)] / [(a-5)(a-2)(a+4)(a+1)]
Now, expand and simplify the numerator:
(a^3 + 6a^2 + 4a + a^2 + 4a + 2 - a^3 + 6a^2 - 11a + 3)(a-5)(a-2)
= (a^3 + a^2 + 10a + 5)(a-5)(a-2)
= (a^4 - 4a^3 + 11a^2 - 35a + 10)
So, the simplified expression is:
(a^4 - 4a^3 + 11a^2 - 35a + 10) / [(a-5)(a-2)(a+4)(a+1)]
Now, let's compare this simplified expression to the given answer choices:
A) -3a-11/(a-5)(a+4)
B) 13a-11/(a-5)(a+4)
C) -3a+19/(a-5)(a+4)
D) a^2-13a-11/(a-5)(a+4)
By comparing the simplified expression to the answer choices, we can see that the correct answer is:
D) a^2-13a-11/(a-5)(a+4)