7. Systems of Equations & Matrices

In Exercises 16–24, write the partial fraction decomposition of each rational expression. x/(x - 3)(x + 2)

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

Answer each question. By what expression should we multiply each side of (3x - 2)/(x + 4)(3x^2 + 1) = A/(x + 4) + (Bx + C)/(3x^2 + 1) so that there are no fractions in the equation?

Answer each question. By what expression should we multiply each side of (3x - 1)/(x(2x^2 + 1)^2) = A/x + (Bx + C)/(2x^2 + 1) + (Dx + E)/(2x^2 + 1)^2 so that there are no fractions in the equation?

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 5/(3x(2x + 1))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. x/(x^2 + 4x - 5)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 4/(x(1 - x))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x + 1)/(x + 2)^3

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^2)/(x^2 + 2x + 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^3 + 4)/(9x^3 - 4x)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-3)/(x^2(x^2 + 5))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x^2 + 1))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x^2 + 4))