Perform the denoted operation.
(4/6x^{2})-(1/3x^{5})+(5/2x^{3})
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 : 6x^{5}
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.
(4/6x^{2})-(1/3x^{5})+5/2x^{3})=4(x^{3})/6x^{2}(x^{3})-(1(2)/3x^{5}(2)+5(3x^{2})/2x^{3}(3x^{2})
=(4x^{3}/6x^{5 })-(2/6x^{5})+(15x^{2}/6x^{5})
= (4x^{3}-2+15x^{2})/6x^{5})