91Ó°ÊÓ

In Exercises \(43-46,\) perform each long division and write the partial fraction decomposition of the remainder term. $$\frac{x^{4}+2 x^{3}-4 x^{2}+x-3}{x^{2}-x-2}$$

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} 2 x^{2}+x y=6 \\ x^{2}+2 x y=0 \end{array}\right.$$

In Exercises \(47-50,\) write the partial fraction decomposition of each rational expression. $$\frac{1}{x^{2}-c^{2}} \quad(c \neq 0)$$

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\\x+y>2\end{array}\right.$$

In Exercises \(47-50,\) write the partial fraction decomposition of each rational expression. $$\frac{a x+b}{x^{2}-c^{2}} \quad(c \neq 0)$$

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x^{2}+y^{2} \leq 4 \\\x+y>1\end{array}\right.$$

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} 4 x^{2}+x y=30 \\ x^{2}+3 x y=-9 \end{array}\right.$$

Solve each system for \(x\) and \(y,\) expressing either value in terms of a or \(b,\) if necessary. Assume that \(a \neq 0\) and \(b \neq 0\). $$\left\\{\begin{aligned}5 a x+4 y &=17 \\\a x+7 y &=22\end{aligned}\right.$$

In Exercises \(47-50,\) write the partial fraction decomposition of each rational expression. $$\frac{a x+b}{(x-c)^{2}} \quad(c \neq 0)$$

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} -4 x+y=12 \\ y=x^{3}+3 x^{2} \end{array}\right.$$