I need help subtracting these fractions:?

Question

x^2 over x - 3 minus 9 over x-3


Also:
5a - 12 over a^2 - 8a = 15 minus 3a - 2 over a^2 - 8a + 15

sorry, the other question I wrote wrong:
5a-12 over a^2 - 8a + 15 minus 3a -2 over a^2 -8a + 15

Answer 1

1. First: both fractions have the same denominator - subtract the numerators & keep them over the denominator...

(x^2 - 9)/x-3

Sec: factor the numerator (you have the difference of squares)...

(x+3)(x-3)/x-3

Third: cross cancel "like" terms to get...

= x + 3

Answer 2

(x squared / x-3) -(9 / x-3) =

x squared - 9 / x - 3 =

(x + 3) (x - 3) / x-3 if you factor the x squared minus 9

then cancel x minus 3 out of the top and bottom

answer remains

Answer = x + 3
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

second problem has something wrong with the way it was
written...cannot see easy solution... however

a sqared minus 8 a factors to a(a-8)
a squared minus 8a + 15 factors to (a-3)(a-5)

so if you look at that problem one more time, maybe you can
do some cancellations and arrive at an easy answer

Answer 3

x^2 over x - 3 minus 9 over x-3

Do you mean this

x^2/(x-3) - 9/(x-3) = x + 3 How did I get this

you have a common denominator of (x-3), so

x^2-9 factor
--------
x-3


(x-3)(x+3)
-------------- = x+3
x-3


5a-12 over a^2 - 8a + 15 minus 3a -2 over a^2 -8a + 15

(5a-12)/(a^2-8a+15) - (3a-2)/(a^2-8a+15) = 2/(a-3) How did I get this

you have a common denominator of (a^2-8a+15), so

(5a-12)-(3a-2)
--------------------
(a^2-8a+15)

5a-12-3a+2
-----------------
(a^2-8a+15)


2a-10 factor
---------------
a^2-8a+15 factor


2(a-5)
--------------
(a-5)(a-3)


2
------
a-3

Answer 4

The first problem is straight forward because it seems that you have common denominators. Sooo...I would guess the numerator is x^2 - 9 and denominator is x - 3. Now if I remember correctly, x^2 - 9 = (x - 3)(x + 3)...remember FOIL...so you will have (x - 3)(x + 3)/(x - 3) --> (x + 3)

Answer 5

my algebra's pretty rusty, but the first one is factoring

x^2/x-3 - 9/x-3
x^2-9/x-3
(x+3)(x-3)/x-3
=x+3 (^^those cancel out)

uhh, the second one will take time. i can't show the work, but it's factoring again. go to webmath.com. they'll solve the equation and show the work.

Answer 6

x^2/(x-3) - 9/(x-3) = (x^2-9)/(x-3) = (x-3)(x+3)/(x-3) = x+3

Answer 7

That seems pretty hard!