SOLUTION: how do i solve algebraically for x: (1/x+3)-(2/3-x)=(4/x^2-9)?

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Question 415634: how do i solve algebraically for x: (1/x+3)-(2/3-x)=(4/x^2-9)?
Answer by lwsshak3(11628) About Me  (Show Source):
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how do i solve algebraically for x: (1/x+3)-(2/3-x)=(4/x^2-9)?
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(1/x+3)-(2/3-x)=(4/x^2-9)
change the sign of the second term and change denominator. Change denominator of right-hand term to a difference of squares:
(1/x+3)+(2/x-3)=(4/(x+3)(x-3))
LCD=(x+3)(x-3)
x-3+2(x+3)=4
x-3+2x+6=4
3x=4-3=1
x=1/3