Two sisters have decided to watch all the episodes of a popular TV show on DVD. Leah has already watched 5 episodes and will continue to watch the show at a rate of 2 episodes per day. Sophia, Who hasn’t yet seen the show, will start watching 3 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How many episodes were each sister and have watched How many episodes each watch that at that point?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).