x x
_____ - _____ = x^2+9
________
x+3 x-3 X^2-9
solve for x. and check answer thank you show work please
To solve for x in the equation:
(x / (x+3)) - (x / (x-3)) = (x^2+9) / (x^2-9)
We can start by multiplying both sides of the equation by (x^2-9) to eliminate the denominators:
(x^2-9) * [(x / (x+3)) - (x / (x-3))] = (x^2-9) * [(x^2+9) / (x^2-9)]
Simplifying this, we get:
x(x-3) - x(x+3) = x^2+9
Expand the brackets:
x^2 - 3x - x^2 - 3x = x^2 + 9
Combine like terms:
-6x = x^2 + 9 - x^2
Cancel out the x^2 terms:
-6x = 9
Now, divide by -6 to solve for x:
x = 9 / -6
Simplifying:
x = -3/2 or -1.5
To check the answer, substitute x = -3/2 or -1.5 back into the original equation and verify if it holds true.