7. Systems of Equations & Matrices

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x²+1) + 2x/(x²+1)².

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^3 + 5x^2 + 7x - 1)/(x^2 + x + 1)^2

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (7x^2 - 7x + 23)/(x - 3)(x^2 + 4)

In Exercises 16–24, write the partial fraction decomposition of each rational expression.3x/(x - 2)(x^2 + 1)

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

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/(x² + 4x - 5)