91Ó°ÊÓ

Write the partial fraction decomposition of each rational expression. $$\frac{5 x^{2}-6 x+7}{(x-1)\left(x^{2}+1\right)}$$

Write the partial fraction decomposition of each rational expression. $$\frac{5 x^{2}-9 x+19}{(x-4)\left(x^{2}+5\right)}$$

Solve each system by the addition method. \(\left\\{\begin{array}{l}5 x-6 y+40 \\ 2 y-8-3 x\end{array}\right.\)

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} x+y^{2}-4 \\ x^{2}+y^{2}-16 \end{array}\right.$$

In Exercises \(29-30,\) solve each system for \((x, y, z)\) in terms of the nonzero constants \(a, b,\) and \(c\) $$ \left\\{\begin{array}{c} a x-b y+2 c z=-4 \\ a x+3 b y-c z=1 \\ 2 a x+b y+3 c z=2 \end{array}\right. $$

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l} 2 x-y \leq 4 \\ 3 x+2 y>-6 \end{array}\right.$$

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l} y>2 x-3 \\ y<-x+6 \end{array}\right.$$

Write the partial fraction decomposition of each rational expression. $$\frac{5 x^{2}+6 x+3}{(x+1)\left(x^{2}+2 x+2\right)}$$

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} 2 x^{2}+y^{2}-18 \\ x y-4 \end{array}\right.$$

Solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(\left\\{\begin{array}{l}x-9-2 y \\ x+2 y-13\end{array}\right.\)