Question

*** I will give you a medal ***
Simplify the difference.
(a^2-2a-3)/(a^2-9a+18) - (a^2-5a-6)/(a^2+9a+8)

Answer 1

@jim_thompson5910

Answer 2

what do you get when you factor a^2-9a+18

Answer 3

(a-6)(a-3)

Answer 4

good, now factor a^2+9a+8

Answer 5

(a+1)(a+8)

Answer 6

I'll factor the numerators:

a^2-2a-3 factors to (a+1)(a-3)

a^2-5a-6 factors to (a+1)(a-6)

Answer 7

so after factoring those 4 expressions, we go from this

(a^2-2a-3)/(a^2-9a+18) - (a^2-5a-6)/(a^2+9a+8)

to this

[ (a+1)(a-3) ]/[ (a-6)(a-3) ] - [ (a+1)(a-6) ]/[ (a+1)(a+8) ]

Answer 8

Notice how in the first fraction, there is a "a-3" in common, so they cancel

Also, in the second fraction, there's a "a+1" in common, that pair cancels to

which gives us this

(a+1)/(a-6) - (a-6)/(a+8)

Answer 9

yes. i got that far. now i just dont know what to do after that. lol.

Answer 10

from here, you need to get the LCD

Answer 11

what is the LCD

Answer 12

48 ?

Answer 13

the denominators of (a+1)/(a-6) - (a-6)/(a+8) are what?

Answer 14

what?

Answer 15

what is the denominator of (a+1)/(a-6)

Answer 16

the (a-6) is the deno right?

Answer 17

good, what's the denominator of (a-6)/(a+8)

Answer 18

(a+8)

Answer 19

so the LCD is _____

Answer 20

48 ?

Answer 21

no you just multiply the denominators, but you don't expand

Answer 22

-48 ?

Answer 23

6x8 is 48

Answer 24

LCD: (a-6)(a+8)

Answer 25

and you leave it like that

Answer 26

ohhh

Answer 27

Now use this to combine the fractions

(a+1)/(a-6) - (a-6)/(a+8)

[(a+1)(a+8)]/[(a-6)(a+8)] - (a-6)/(a+8)

[(a+1)(a+8)]/[(a-6)(a+8)] - [(a-6)(a-6)]/[(a-6)(a+8)]

[(a+1)(a+8) - (a-6)(a-6)]/[(a-6)(a+8)]

[a^2 + 9a + 8 - (a^2 - 12a + 36)]/[(a-6)(a+8)]

[a^2 + 9a + 8 - a^2 + 12a - 36]/[(a-6)(a+8)]

[21a - 28]/[(a-6)(a+8)]

Answer 28

thanks (: