Solve for X?

Question

solve for x 1/x+3 = x+1/x^2-9 thanks for your help

Answer 1

Be careful of your order of operations... toss in parentheses if they're needed to better state the problem here.

I'm assuming your problem is:
1 / (x - 3) = (x + 1) / (x² - 9)
Factor the denominator.
1 / (x - 3) = (x + 1) / [(x + 3)(x - 3)]
Multiply both sides by [(x + 3)(x - 3)] to get rid of the fractions.
(x + 3)(x - 3) / (x - 3) = (x + 1)(x + 3)(x - 3) / [(x + 3)(x - 3)]
Cancel common factors. [Remember, this problem has excluded values... the denominator of any fraction can never be zero, so x ≠ ±3.]
x + 3 = x + 1
Subtract x from both sides.
3 = 1.
This is a false statement, so this problem has no solutions. Sorry... maybe my assumption was wrong.

Answer 2

Assume you meant

1/(x + 3) = (x + 1)/(x^2 - 9)

The denominators are (x + 3) and (x^2 - 9) and the latter factors into (x + 3)(x - 3) so multiply both sides by this common denominator

Both old denominators now disappear and we are left with

x - 3 = x + 1 or -3 = 1 ... no solution here!

If I interpret the problem exactly as written, where the only fractions are 1/x and 1/x^2, and multiply both sides by x^2, I get

x + 3x^2 = x^3 + 1 - 9x^2

x^3 - 12x^2 - x + 1 = 0

For now, I guess this is not what you had in mind

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I see that another party offerred the answer x = - 3

Please note that if you put this result into your original equation you end up dividing by zero, which is undefined, so there really is no solution!

Answer 3

This isn't answerable at the moment because it is not possible to tell if the last bit is x^(2-9) or (x^2)-9, and even then, is the 9 a part of the denominator or is it a separate piece?

Answer 4

if the problem is 1/(x+3)=(X+1)/(X^2-9), THEN

1) cross multiply

x^2-9=(x+3)(x+1)

2) FOIL

x^2-9=x^2+3x+x+3

3) Combine Like Terms and bring all terms to one side of the equation:

x^2-x^2-4x-9-3=0
0-4x-12=0
-4x=12
x=-3,

so, x= -3

Answer 5

1/(x + 3) = (x + 1)/(x^2 - 9)
(x + 3)(x + 1) = x^2 - 9
(x + 3)(x + 1) = (x + 3)(x - 3)
x + 1 = x - 3
0x = -4
x = -4/0

x is undefined.

Answer 6

No solution.