Question

Ok so from what I know you begin to solve: [(x^+2x)/(12x+54)]-[(3-x)/(8x+36)] by distributing the negative : [(-3+x)/(8x+36)] and then factoring both the denominators 8x+35=4(2x+9) and 12x+54=6(2x+9)

so no i have:

[(x^2+2x)/(6(2x+9))]+[(-3+x)/(4(2x+9))]

now the one on the left is missing 4 and the one on the right is missing 6 right so you multiply and get:

[(4x^2+8x)/(24(2x+9))]+[(6x-18)/(24(2x+9))]

add the numerators because they share a denominator:

(4x^2+14x-18)/(24(2x+9))

lcm= 2 so you factor

2(2x^2+7x-9)/24(2x+9)

simplify..
(2x^2+7x-9)/12(2x+9)

ok so what h

Answer 1

wolframalpha.com (it answers these problems) says the answers (x-1)/(12)

Answer 2

did you try factoring
(2x^2+7x-9)

Answer 3

(2x^2+7x-9)
you know that you want something like
(x+a)(x+b)
now when you foil that out notice that we need to wind up with a coefficient of 2 on the x^2 term, so that means one of our factors will have a 2x in it (since the only factors of 2 are 2 and 1)
so it should look like
(2x^2+7x-9)
(2x+a)(x+b)
now we need to find a and b
again if we foil this out it should be clear that we want ab=-9, so what are the factors of -9 ? try those for a and b and see which gets the correct cross term of 7

Answer 4

(2x^2+7x-9)
(2x+a)(x+b)
foiling this out we get
2x^2+(a+2b)x+ab
we need a+2b=7 and ab=-9 for the correct factorization, so find the correct a and b such that that works

Answer 5

it basically comes down to solving
a+2b=7
ab=-9

Answer 6

remember we want the factors of -9, not 9

Answer 7

a and/or b could be negative, so don't worry about the + sign

Answer 8

the factorisation of (2x^2+7x-9) will be (2x+a)(x+b) and we need to find a and b, agreed?

Answer 9

(2x+a)(x+b)=2x^2+ax+2bx+ab=2x^2+(a+2b)x+ab
so
a+2b=7
ab=-9

let's go down your list of factorizations of -9
the first one you have is -1 and 9, so try a=-1 and b=9, or a=9 and b=-1 and see of that gets the right cross term of 7x

Answer 10

another way to do it would be to just solve the system
a+2b=7
ab=-9

Answer 11

you chose a=1 and b=3, but 1*3 is not -9
you need to chose a and b that are factors of -9

Answer 12

you made a list, try those values...
1,-9
3,-3
-1,9
those are your three options

Answer 13

you cannot choose 3 and one because that does not multiply to -9
they *must* multiply to -9
here are your options
-1,9
3,-3
1,-9
so there are six possibilities:
a=-1,b=9
a=3,b=-3
a=1,b=-9
or the other way around
b=-1,a=9
b=3,a=-3
b=1,a=-9
try them until you find which one works
(with time you will be able to do it faster in your head)

Answer 14

oh ok sorry, i see now, (9)+2(-1)=7,(9)(-1)=-9

Answer 15

yes :)
so the factorization is...?

Answer 16

(2x+9)(x-1)/12(2x+9)=(x-1)/(12)

Answer 17

quite welcome :)