Basic Algebra?

Question

I cannot figure this problem out and I dont understand why. Plz explain. Only have to give answer if you feel like it. If not the way of figuring it is greatly appreciated.

Simplify (15x^2 - 24x + 9) / (3x - 3)

Answer 1

top and bottom both divisible by 3
= (5x^2 -8x + 3) / (x-1) .. note top is quadratic
= [ (x-1)(ax+b) + c ] /(x-1) ... we want to find a,b,c
= [ a x^2 + (b-a)x +(c-b) ] /(x-1) ... compare x^2 terms .. a must be 5
= [ 5 x^2 +(b-5)x +(c-b) ] / (x-1) .. compare x terms .. b must be -3
= [ 5 x^2 -8 x +( c+3) ] / (x-1) ... surprise surprise, c must be 0
= ( x-1 ) (5x-3) / (x-1)
= 5x-3

Answer 2

(15x^2 - 24x + 9) / (3x - 3)

factorizing
(15x^2 - 15x - 9x +9) / [3(x-1)]
[15x(x - 1) -9(x - 1)] / [3(x-1)]
[(x - 1)(15x - 9)] / [3(x-1)]

(x - 1) will be canceled
(15x - 9) / 3
(15x/3) - (9/3)
5x -3
which is your answer


Basic Algebra:

We can factorize numerator by this process
step1: First multiply coefficient of x^2 and constant term (9*15)
step2: Factorize this answer (135=3*3*3*5)
step3: Set these numbers in two teams and this setting should be as on adding or subtracting we get coefficient of x (-9-15)

Answer 3

(15x^2 - 24x + 9) / (3x - 3)

Factor the numerator
(3x-3)(5x-3)/(3x-3)
so the 3x-3 cancel so our answer
5x-3

Answer 4

i think the question is wrong it should be (15x^2-24x-9)/(3x-3)
if u hav typed the question correctly then the quotient is 5x+3
and the remainder is 18

Answer 5

15x² - 24x + 9
------------------ =
3x - 3

(5x - 3)(3x - 3)
- ------------------- . . ..3x - 3 cancell
3x - 3

5x - 3

- - - - - - - -s-

Answer 6

(3x-3)(5x-3)/(3x-3)

Cancel out the (3x-3):
5x-3

I hope this helps!