SOLUTION: solve: 3x over x^2-1=5 over x

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Question 187683This question is from textbook saxon algebra 2
: solve: 3x over x^2-1=5 over x This question is from textbook saxon algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%29%2F%28x%5E2-1%29=5%2Fx Start with the given equation.


%283x%29%28x%29=5%28x%5E2-1%29 Cross multiply


%283x%29%28x%29=5%28x%5E2%29-5%281%29 Distribute


3x%5E2=5x%5E2-5 Multiply


3x%5E2-5x%5E2=-5 Subtract 5x%5E2 from both sides.


-2x%5E2=-5 Combine like terms.


x%5E2=%28-5%29%2F%28-2%29 Divide both sides by -2.


x%5E2=5%2F2 Reduce


x=sqrt%285%2F2%29 or x=-sqrt%285%2F2%29 Take the square root of both sides (keep in mind that there are two possible options here)


x=sqrt%285%29%2Fsqrt%282%29 or x=-sqrt%285%29%2Fsqrt%282%29 Break up the square root.


x=%28sqrt%285%29%2Asqrt%282%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29 or x=-%28sqrt%285%29%2Asqrt%282%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29 Multiply the numerator and denominator by sqrt%282%29 (to rationalize the denominator)


x=sqrt%2810%29%2F2 or x=-sqrt%2810%29%2F2 Combine the roots and multiply

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Answer:


So the solutions are x=sqrt%2810%29%2F2 or x=-sqrt%2810%29%2F2