SOLUTION: 4) Solve. (n over n-4/9) -(n over n+4/9)= (1 over n) Pretty please will someone help me solve this? :)

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: 4) Solve. (n over n-4/9) -(n over n+4/9)= (1 over n) Pretty please will someone help me solve this? :)      Log On

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Question 199246: 4) Solve. (n over n-4/9) -(n over n+4/9)= (1 over n)
Pretty please will someone help me solve this? :)
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
n%2F%28n-4%2F9%29-n%2F%28n%2B4%2F9%29=1%2Fn Start with the given equation.



n%2F%28%281%2F9%29%289n-4%29%29-n%2F%28%281%2F9%29%289n%2B4%29%29=1%2Fn Factor out 1%2F9 (to make the inside terms have whole numbers)



%289n%29%2F%289n-4%29-%289n%29%2F%289n%2B4%29=1%2Fn Multiply both the numerator and denominator by the reciprocal of 1%2F9



Multiply every term on both sides by the LCD n%289n-4%29%289n%2B4%29. Doing this will eliminate all of the fractions.


n%289n%2B4%29%289n%29-n%289n-4%29%289n%29=%289n-4%29%289n%2B4%29 Simplify


9n%2An%289n%2B4%29-9n%2An%289n-4%29=%289n-4%29%289n%2B4%29 Rearrange the terms.


9n%5E2%289n%2B4%29-9n%5E2%289n-4%29=%289n-4%29%289n%2B4%29 Multiply


81n%5E3%2B36n%5E2-81n%5E3%2B36n%5E2=%289n-4%29%289n%2B4%29 Distribute


72n%5E2=%289n-4%29%289n%2B4%29 Combine like terms.


72n%5E2=81n%5E2-16 FOIL


72n%5E2-81n%5E2=-16 Subtract 81n%5E2 from both sides.


-9n%5E2=-16 Combine like terms.


n%5E2=-16%2F%28-9%29 Divide both sides by -9.


n%5E2=16%2F9 Reduce


n=%27%27%2B-sqrt%2816%2F9%29 Take the square root of both sides.


n=sqrt%2816%2F9%29 or n=-sqrt%2816%2F9%29 Break up the "plus/minus"


n=4%2F3 or n=-4%2F3 Take the square root of 16%2F9 to get 4%2F3



So the solutions are n=4%2F3 or n=-4%2F3