91Ó°ÊÓ

Solve each system. Use any method you wish. $$ \left\\{\begin{array}{c} \ln x=5 \ln y \\ \log _{2} x=3+2 \log _{2} y \end{array}\right. $$

Solve each system of equations. If the system has no solution, state that it is inconsistent. $$ \left\\{\begin{array}{r} x-y+z=-4 \\ 2 x-3 y+4 z=-15 \\ 5 x+y-2 z=12 \end{array}\right. $$

Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. $$ \frac{x^{3}+x}{x^{2}+4} $$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. $$ \left\\{\begin{array}{r} 2 x-3 y-z=0 \\ -x+2 y+z=5 \\ 3 x-4 y-z=1 \end{array}\right. $$

Solve for \(x\) \(\left|\begin{array}{rrr}3 & 2 & 4 \\ 1 & x & 5 \\ 0 & 1 & -2\end{array}\right|=0\)

Solve each system of equations. If the system has no solution, state that it is inconsistent. $$ \left\\{\begin{array}{r} x+2 y-z=-3 \\ 2 x-4 y+z=-7 \\ -2 x+2 y-3 z=4 \end{array}\right. $$

Solve for \(x\) \(\left|\begin{array}{rrr}x & 2 & 3 \\ 1 & x & 0 \\ 6 & 1 & -2\end{array}\right|=7\)

Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. $$ \frac{x^{4}-5 x^{2}+x-4}{x^{2}+4 x+4} $$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. $$ \left\\{\begin{array}{rr} -x+y+z= & -1 \\ -x+2 y-3 z= & -4 \\ 3 x-2 y-7 z= & 0 \end{array}\right. $$

Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. $$ \frac{x^{4}+x^{3}-x+2}{x^{2}-2 x+1} $$