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
how to use fraction busters?
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.