Evaluate w+(-x)-\dfrac{2}{3}w+(−x)− 3 2 w, plus, left parenthesis, minus, x, right parenthesis, minus, start fraction, 2, divided by, 3, end fraction where w = -\dfrac{5}{9}w=− 9 5 w, equals, minus, start fraction, 5, divided by, 9, end fraction and x = \dfrac{4}{3}x= 3 4 x, equals, start fraction, 4, divided by, 3, end fraction.

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).