HELP finding partial fraction decomposition? (PIC INCLUDED)

Question

anonymous · Answer

attachment

anonymous · Answer

@satellite73

anonymous · Answer

@Hero  help me pleaseee??

anonymous · Answer

@ash2326  can you help me?

ash2326 · Answer

We have 
$$\frac{5}{3x^2-x-2}$$
Can you factor the denominator?

anonymous · Answer

yes i got (x-3)(x+2)

ash2326 · Answer

Check again, there is some mistake. Try multiplying this, are you getting the denominator?

anonymous · Answer

i factored denominator

ash2326 · Answer

$$(x-3)(x+2)=x^2-x-6\ne 3x^2-x-2$$

anonymous · Answer

oh so what does tht factor into then??

ash2326 · Answer

$$3x^2-x-2$$
$$3x^2-3x+2x-2$$
$$3x(x-1)+2(x-1)$$
Can you find now?

anonymous · Answer

ok so thats the answer for denomiator?

anonymous · Answer

its a partial fraction denominator i dont know what that is

ash2326 · Answer

It's to be factored, just one more step

anonymous · Answer

i meant  partial fracton decompostion

ash2326 · Answer

We'll work on that, could you write the two factors

anonymous · Answer

what you just put for that equation?

ash2326 · Answer

I suppose those are not factors, please do one more step and write the two factors

anonymous · Answer

(x-1)(x-1) ??

ash2326 · Answer

Have you studied factoring? @idreamofpink

anonymous · Answer

yes i have but not partial fractoin decomposition. im just at a lost.

anonymous · Answer

im tryna figure out what the answer is and i just have no clue.

ash2326 · Answer

We'll work on that, please just factor this
$$3x^2-x-2$$

anonymous · Answer

i honestly don know how that can be factored.

ash2326 · Answer

$$3x^2-x-2$$
Can you write factors of -6? which add to -1

anonymous · Answer

-3 and 2

ash2326 · Answer

Good so
$$3x^2-3x+2x-2$$
Can you take common out of the first two and last two terms?

ash2326 · Answer

I'll brb

anonymous · Answer

yes 1

ash2326 · Answer

So Did you work it out?

anonymous · Answer

isnt gona be same answer

anonymous · Answer

i need step by step i dont know what to do. -_-

anonymous · Answer

@ash2326  ?

jhannybean · Answer

So you have  $\large 3x^2-3x+2x-2$ which = $\large 3x^2 -x - 2$ right ?

jhannybean · Answer

Factor out like terms and simplify by grouping$$\large (\color{green}{3x}^2 - 3x )+(\color{blue}2x-2) $$ can you tellme what you get when you factor out like terms from these two groups?

anonymous · Answer

yewa i already skipped that question tho.. but thanks anyway

jhannybean · Answer

Why skip it when we can help you solve it? :)

anonymous · Answer

i already skipped it before you replied but can you help me with another question?

jhannybean · Answer

Well, if you have a calc book you can look up partial fractions in your index...

jhannybean · Answer

I can try, but i have to go soon. I'll start you off.