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how to use fraction busters?

well my teacher tried to teach our class fraction busters or like when you multiply 1 over x plus 3x over 2 = x over 5 or something like that. I didnt realy get the concept so if i could get some tips or easy to understand ways to do it that would be much apreciated 

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Jean-Guy L. | Experienced Tutor in KentExperienced Tutor in Kent
4.9 4.9 (232 lesson ratings) (232)

Ok let us start by changing the equation you gave: 1/x -  3x/2 = x/5 (I just changed the sign of 3x/2)

To solve the equation, it is always good to group terms with the same power of x. The 1/x is a power -1 of x or x^-1 while the other terms are a power +1 of x or x^1. By grouping the terms in x (of power 1), we get the equation:

1/x = x/5 + 3x/2 

1/x = (1/5 + 3/2) x

1/x = (17/10) x -> multiply by x each side

1 = (17/10) x^2 -> multiply by 10/17 each side

10/17 = x^2 -> take the square root each side

There are 2 solutions +sqrt(10/17) = x and -sqrt(10/17) = x

Note: the equation you gave had no real solutions, but only complex, so I changed it to get real solutions.