-5/x-3 - 3/x+3 = 2/x^2-9
You said to divide by 9 on both sides
9(x+3)-3(x+3)=2
9x+27-3+9=2
6x=36
6x=48
x=8
Is this correct? Thanks for your help.
Actually, there seems to be a mistake in the algebraic manipulation. Let's go through the correct steps to solve the equation.
The starting equation is:
-5/(x-3) - 3/(x+3) = 2/(x^2-9)
To simplify the equation, we first need to find a common denominator for the fractions on the left side. The common denominator in this case is (x-3)(x+3) because (x-3)(x+3) = x^2 - 9.
The equation then becomes:
(-5(x+3))/(x-3)(x+3) - (3(x-3))/(x-3)(x+3) = 2/(x^2-9)
Now, we can combine the numerators over the common denominator:
(-5(x+3) - 3(x-3))/(x-3)(x+3) = 2/(x^2-9)
Simplifying the numerators:
(-5x - 15 - 3x + 9)/(x-3)(x+3) = 2/(x^2-9)
(-8x - 6)/(x-3)(x+3) = 2/(x^2-9)
To eliminate the denominators, we can multiply both sides of the equation by (x-3)(x+3):
(x-3)(x+3)*(-8x - 6)/(x-3)(x+3) = (x-3)(x+3)*2/(x^2-9)
Cancelling out the denominators:
-8x - 6 = 2
Now, we can proceed to solve for x:
-8x - 6 = 2
-8x = 2 + 6
-8x = 8
x = 8/(-8)
x = -1
Therefore, the correct solution to the equation is x = -1, not x = 8 as you mentioned earlier.