7. Systems of Equations & Matrices

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)

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. (x²)/(x² + 2x + 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x³ + 4)/(9x³ - 4x)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-3)/(x²(x² + 5))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x² + 1))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x² + 4))

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x⁵ + 3x⁴ - 3x³ - 2x² + x)/(2x² + 5x + 2)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 1)/(x(2x² + 1)²)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x⁴ - 8x² + 3x - 10)/((x + 2)(x² + 4)²)