3/(a^2-5x+6)=3/(a-3)-2/(a-2)

- anonymous

3/(a^2-5x+6)=3/(a-3)-2/(a-2)

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- anonymous

Can someone please help me solve this
|dw:1370541304507:dw|

- Xanthe

First, make the base on the RHS to be the same then rearrange the equation to solve for a

- anonymous

ok so I multiply the rhs by x+6?

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## More answers

- anonymous

i don't think there's an answer but I'm not sure how to prove it

- anonymous

heello?

- Xanthe

Wait.. where in the world did x come from?@@

- Xanthe

Shouldnt it be a?

- anonymous

nope

- anonymous

it's x

- anonymous

so @Xanthe what should I do?

- Xanthe

Ok so what is the question asking?
To find a or x?

- anonymous

it just says solve the equation @Xanthe

- Xanthe

And you are sure there are 2 variables a and x?

- anonymous

|dw:1370542193093:dw|

- anonymous

that's exactly as it shows it^

- Xanthe

Ok well try to solve the Right Hand Side first(RHS).Show me your workings
|dw:1370542171263:dw|

- Xanthe

U there?

- anonymous

yes

- anonymous

I got

- anonymous

|dw:1370542534148:dw|

- anonymous

so wouldn't it end up being 2a-3a=-a

- anonymous

right?

- Xanthe

Ohh..now i get it..

- Xanthe

Ok show me your workings n nt jus the answers.I want to know hw u derived to get them

- anonymous

I didn't get any answers

- anonymous

my answer is no solution, and need help proving it

- Xanthe

How did u get this?
|dw:1370542941289:dw|

- anonymous

you said try to solve the rhs so I tried to make them have common denominators but couldn't

- anonymous

|dw:1370543069971:dw|

- Xanthe

Ok.. look at my working n try to expand the bottom part.
|dw:1370543059484:dw|
Once youve done that,compare with the LHS

- Xanthe

Ive make both the bases the same (a-2)(a-3)

- Xanthe

Expand the base (a-2)(a-3) and then u can do the comparison with the LHS

- anonymous

what do u mean expand the base @Xanthe

- Xanthe

|dw:1370543711922:dw|

- anonymous

oh, a^2-3a+-2a-6

- anonymous

is that right

- anonymous

\[x=\frac{a^3-3 a^2+21 a-18}{5 a} \]

- Xanthe

Simplify..

- anonymous

a^2-a-6

- Xanthe

@robtobey u solving for x?@.@

- anonymous

no ur suppose to solve the equation

- Xanthe

Really @aprilsages

- anonymous

I am pretty sure it's no solution, just need to prove it

- anonymous

lol yes @Xanthe

- Xanthe

Do you know how to expand?

- anonymous

yes

- Xanthe

Check w mine
|dw:1370543978832:dw|

- anonymous

Yes, I posted the solution for x.

- anonymous

oh whoops, simple error, my bad

- Xanthe

Lol I dont think u hv to go solve for x @robtobey.Its just comparing the LHS and RHS rgt?

- Xanthe

@aprilsages u know hw to go from there?

- anonymous

no

- Xanthe

Lol.Ok see any resemblance?
|dw:1370544312781:dw|

- Xanthe

Youve might have guessed from here what a and x is..

- anonymous

lol ya but how can x=a?

- anonymous

they'd be the same ariable then

- anonymous

*variable

- anonymous

@Xanthe u there?

- Xanthe

That the point of it Im afraid.
So x=a=3.
Lol.But it make sense cos if u substitute x=a=3 on both the
LHS & RHS,
LHS=RHS
0=0

- Xanthe

N if u still cant figure out why, Substitute a=3 into the equation that @robtobey has kindly given and youll found x to be 3..So yea..

- Jhannybean

|dw:1370544949622:dw|

- anonymous

@Jhannybean can x=a=3

- Jhannybean

|dw:1370544994035:dw|

- anonymous

@Jhannybean there's no solution @Xanthe

- anonymous

i plugged it into the original and it doesn't work

- Xanthe

What do u mean it doesnt work?

- anonymous

@Jhannybean it's 5x not 5a

- Jhannybean

oh crap. -_-

- Xanthe

How do u get
|dw:1370545788507:dw|
@Jhannybean

- Xanthe

lol

- anonymous

no ppl it's 5x :( i want to say no solution

- Jhannybean

it's no solution.

- anonymous

but whats the equation or work i can show to prove it

- Jhannybean

because if you solved for the denominators on the LHS
a - 3 = 0
a - 2 = 0
and this means that the function is discontinuous at 3 and 2.
When you're solving the equation on the RHS for a, you're only getting the answer with a = 3, which doesn't make sense.

- Xanthe

ikr

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