7. Systems of Equations & Matrices

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)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x²)/(x⁴ - 1)

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

Find the partial fraction decomposition for each rational expression. 5-2x / (x² + 2)(x - 1)

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w + 2x + 3y - z = 7 \\2x - 3y + z = 4 \\w - 4x + y = 3\end{cases}$