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Chapter 5: Problem 4
Determine if the given ordered triple is a solution of the system. $$\begin{aligned} &(-1,3,2)\\\ &\left\\{\begin{aligned} x-2 z &=-5 \\ y-3 z &=-3 \\ 2 x-z &=-4 \end{aligned}\right. \end{aligned}$$
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write the partial fraction decomposition of each rational expression. $$ \frac{4}{2 x^{2}-5 x-3} $$
What is an objective function in a linear programming problem?
Solve: $$\left\\{\begin{array}{r} A+B=3 \\ 2 A-2 B+C=17 \\ 4 A-2 C=14 \end{array}\right.$$
determine whether each statement makes sense or does not make sense, and explain your reasoning. I apply partial fraction decompositions for rational expressions of the form \(\frac{P(x)}{Q(x)},\) where \(P\) and \(Q\) have no common factors and the degree of \(P\) is greater than the degree of \(Q .\)
Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$ Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$
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