Perform the denoted operation.

                   (4/6x²)-(1/3x⁵)+(5/2x³)

Solution

For this problem there are coefficients on each of term in the denominator thus we'll first required the least common denominator for the coefficients. It is 6. Now, x (by itself along a power of 1) is the only factor which occurs in any of the denominators. Thus, the least common denominator for this part is x along with the largest power which occurs on the entire x's in the problem, that is 5.  So, the least common denominator for this set of rational expression is

                                                     lcd : 6x⁵

Thus, we just need to multiply each term via an appropriate quantity to get this in the denominator and then do the addition & subtraction. Let's do that.

 (4/6x²)-(1/3x⁵)+5/2x³)=4(x³)/6x²(x³)-(1(2)/3x⁵(2)+5(3x²)/2x³(3x²)

                                    =(4x³/6x⁵ )-(2/6x⁵)+(15x²/6x⁵)             

                                    = (4x³-2+15x²)/6x⁵)