Question

Which is the quotient and remainder, written as partial fractions, of startfraction x squared 8 over x squared minus 5 x 6 endfraction? 1 minus startfraction 17 over x minus 3 endfraction startfraction 12 over x minus 2 endfraction x minus startfraction 7 over x minus 3 endfraction startfraction 5 over x minus 2 endfraction 1 startfraction 17 over x minus 3 endfraction minus startfraction 12 over x minus 2 endfraction startfraction 7 over x minus 3 endfraction startfraction 5 over x minus 2 endfraction

Answer 1

The quotient in partial fractions is 1 - (17/(x-3)) + (12/(x-2)), and the remainder is (7/(x-3)) - (5/(x-2)).

Step-by-step explanation:

To find the quotient and remainder in partial fractions, we can use the method of polynomial long division. In this case, the numerator is x^2 + 8 and the denominator is x^2 - 5x + 6.

By performing the long division, we get the quotient as 1 - rac{17}{x-3} + rac{12}{x-2} and the remainder as rac{7}{x-3} - rac{5}{x-2}.