how to use fraction bustersSolutionOk let us start by changi

how to use fraction busters?

Solution

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.