Blitzer - College Algebra 8th Edition

Ch. 5 - Systems of Equations and Inequalities

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Section 5.3

Problem 16

Write the partial fraction decomposition of each rational expression. x/(x² +2x -3)

Problem 17

Write the partial fraction decomposition of each rational expression. 4x²+13x-9/x (x − 1)(x+3)

Problem 19

Write the partial fraction decomposition of each rational expression. 4x² - 7x - 3/(x³ -x)

Problem 21

Write the partial fraction decomposition of each rational expression. (6x-11)/(x − 1)²

Problem 23

Write the partial fraction decomposition of each rational expression. (x²-6x+3)/(x − 2)³

Problem 25

Write the partial fraction decomposition of each rational expression. x²+2x+7/x(x − 1)²

Problem 27

Write the partial fraction decomposition of each rational expression. x²/(x − 1)² (x + 1)

Problem 29

Write the partial fraction decomposition of each rational expression. 5x² -6x+7/(x − 1) (x² + 1)

Problem 31

Write the partial fraction decomposition of each rational expression. 5x²+6x+3/(x + 1)(x² + 2x + 2)

Problem 33

Write the partial fraction decomposition of each rational expression. x+4/x² (x²+4)

Problem 35

Write the partial fraction decomposition of each rational expression. 6x²-x+1/(x³ + x²+ x +1)

Problem 37

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

Problem 39

Write the partial fraction decomposition of each rational expression. (x³-4x²+9x-5)/(x² -2x+3)²

Problem 41

Write the partial fraction decomposition of each rational expression. (4x²+3x+14)/(x³ - 8)

Problem 43

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁵+2)/(x²-1)

Problem 45

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁴-x²+2)/(x³-x²)

Section 5.4

Problem 3

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} x + y = 2 \\ y = x^2 - 4x + 4 \end{cases}$

Problem 5

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} y = x^2 - 4x - 10 \\ y = -x^2 - 2x + 14 \end{cases}$

Problem 7

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} x^2 + y^2 = 25 \\ x - y = 1 \end{cases}$

Problem 9

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} xy = 6 \\ 2x - y = 1 \end{cases}$

Problem 11

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} y^2 = x^2 - 9 \\ 2y = x - 3 \end{cases}$

Problem 13

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} xy = 3 \\ x^2 + y^2 = 10 \end{cases}$

Problem 15

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} x + y = 1 \\ x^2 + xy - y^2 = -5 \end{cases}$

Problem 17

In Exercises 1–18, solve each system by the substitution method. $\begin{cases} x + y = 1 \\ (x - 1)^2 + (y + 2)^2 = 10 \end{cases}$

Problem 19

In Exercises 19–28, solve each system by the addition method. $\begin{cases} x^2 + y^2 = 13 \\ x^2 - y^2 = 5 \end{cases}$

Problem 21

In Exercises 19–28, solve each system by the addition method. $\begin{cases} x^2 - 4y^2 = -7 \\ 3x^2 + y^2 = 31 \end{cases}$

Problem 23

In Exercises 19–28, solve each system by the addition method. $\begin{cases} 3x^2 + 4y^2 - 16 = 0 \\ 2x^2 - 3y^2 - 5 = 0 \end{cases}$

Problem 25

In Exercises 19–28, solve each system by the addition method. $\begin{cases} x^2 + y^2 = 25 \\ (x - 8)^2 + y^2 = 41 \end{cases}$

Problem 27

In Exercises 19–28, solve each system by the addition method. $\begin{cases} y^2 - x = 4 \\ x^2 + y^2 = 4 \end{cases}$

Problem 29

In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} 3x^2 + 4y^2 = 16 \\ 2x^2 - 3y^2 = 5 \end{cases}$