Adv. Algebra 2 help -- what do I do from where I am?

Question

x/(x2 - 9) + 4/(x+3) = 3/(x2-9)

[x2 means x to the second power.] What I have done so far is multiply all three numbers by x2-9 so I can get rid of the annoying fractions. But, after I do that the problem looks like:

x + 4/(x3-6x-27) = 3 And I don't know where to go from there. Can someone please tell me what to do, or show me what I did wrong, or explain the steps or something? I'm having a similar problem with a problem like:

0.9t = 1 + t. It's so simple I feel like an idiot but I don't know what to do. I try to divide everything by t but then it just doesn't make any sense and the answers I get when I plug them in aren't right. Help, please?

Answer 1

(x² - 9) = (x + 3) (X - 3)

So you got a good start, but need to check the multiplication.  Each of the three terms will cancel part of the (x² - 9).  Instead of (x² - 9), multiply by (x + 3) (x - 3)

It should look like this:

x + [4 (x + 3) (x - 3) ] / (x + 3) = 3

The (x + 3)  should cancel out of both denominator and numerator:

x + 4(x - 3) = 3

It should be pretty easy for you from here:

x + 4x - 12 = 3

5x = 9

x = 9/5

On the second one, start by collecting like terms.  In other words, get the t's together on one side and the numbers on the other:

Subtract 0.9t from both sides:

0.9t -0.9t = 1 + t -0.9t

Combine the t's:

0 = 1 + 0.1 t

Subtract 1 from both sides:

0 - 1 = 1 - 1 + 0.1 t

-1 = 0.1 t

Divide by 0.1:

-1 / 0.1 = 0.1 t / 0.1

1/0.1 = 10 (You can check this on a calculator or multiply both top and bottom of fraction by 10)

So the answer is:

-10 = t or if you prefer t = -10

Answer 2

ok.. i DONT kno if my answer makes sence..but here it goes...

x/(x^2-9) + 4/(x+3) = 3/(x^2-9)

why dont u change the middle part... instead of trying to divide by all (x^2-9) .. change the 4/(x+3) to 4x-3/(x^2-9) by multiplying 4/(x+3) by (x-3).

and then.. u can now divided all the fractions by (x^2-9) and get rid of it..

lastly u solve x+4x-3=3

which is easy...

x+4x-3=3

=> 5x=3+3

=> 5x=6

therefore x= 6/5 or 1,1/5