The equation 9+12m=6+15(m-1) models the following situation: Movie-rental company A charges a sign-up fee of $9 plus $12 per month, and company B charges $6 for the first month plus $15 per month after that. At a certain number of months, the cost of the two companies is equal. Which equation is a simplified version of the one above? 3m = 15 9 + 15m = 12m – 1 3m = 18 9 + 6 – 15 = 15m – 12m

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).