Least common denominator of rational expression, Mathematics

Assignment Help:

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)


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