7. Systems of Equations and Inequalities

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (6x^2-14x-27)/(x+2) (x − 3)^2

Answer each question. By what expression should we multiply each side of (3x - 2)/(x + 4)(3x^2 + 1) = A/(x + 4) + (Bx + C)/(3x^2 + 1) so that there are no fractions in the equation?

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (3x+16)/(x + 1) (x − 2)²

Answer each question. By what expression should we multiply each side of (3x - 1)/(x(2x^2 + 1)^2) = A/x + (Bx + C)/(2x^2 + 1) + (Dx + E)/(2x^2 + 1)^2 so that there are no fractions in the equation?

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (7x^2 -9x+3)/(x²+7)²

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x/(x-2)(x-3)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. x/(x^2 + 4x - 5)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (7x-4)/(x^2-x-12)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 4/(x(1 - x))

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 9x+21/(x² + 2x - 15)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))

In Exercises 16–24, write the partial fraction decomposition of each rational expression. x/(x - 3)(x + 2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4x^2+13x-9/x (x − 1)(x+3)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x + 1)/(x + 2)^3

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4x² - 7x - 3/(x^3 -x)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (x^2-6x+3)/(x − 2)³

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^3 + 5x^2 + 7x - 1)/(x^2 + x + 1)^2

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x²+2x+7/x(x − 1)^2

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x^2 + 1))

In Exercises 9–42, write the partial fraction decomposition of each rational expression.5x^2+6x+3/(x + 1)(x² + 2x + 2)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 1)/(x(2x^2 + 1)^2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x+4/x² (x²+4)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^2)/(x^4 - 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (x^3-4x^2+9x-5)/(x^2 -2x+3)^2

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - 3x - 4)/(x^3 + x^2 - 2x)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (4x^2+3x+14)/(x^3 - 8)

Find the partial fraction decomposition for each rational expression. 2 / 3x^2 - 5x + 2

Find the partial fraction decomposition for each rational expression. 5-2x / (x^2 + 2)(x - 1)

Find the partial fraction decomposition for 1/x(x+1) and use the result to find the following sum:

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: 3/(x−4) − 2/(x+2).

Find the partial fraction decomposition of 4x²+5x-9/(x³- 6x-9)

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. x^3 + x² /(x² + 4)^2

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (3x +50)/(x -9)(x +2)

In Exercises 16–24, write the partial fraction decomposition of each rational expression. x/(x - 3)(x + 2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x/(x^2 +2x -3)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (6x-11)/(x − 1)²

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (7x^2 - 7x + 23)/(x - 3)(x^2 + 4)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-3)/(x^2(x^2 + 5))

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 5x^2 -6x+7/(x − 1) (x² + 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x^4 - 8x^2 + 3x - 10)/((x + 2)(x^2 + 4)^2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^3+x^2+2/(x² + 2)²

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

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 5x²-6x+7 /(x − 1) (x² + 1)

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. x^3 + x² /(x² + 4)^2

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 5/(3x(2x + 1))

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 1/x(x-1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4/(2x^2 -5x -3)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (2x^2 -18x -12)/x³- 4x

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (6x-11)/(x − 1)²

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^3 + 4)/(9x^3 - 4x)

In Exercises 16–24, write the partial fraction decomposition of each rational expression.3x/(x - 2)(x^2 + 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^2/(x − 1)² (x + 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 5x^2 -6x+7/(x − 1) (x² + 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x^5 + 3x^4 - 3x^3 - 2x^2 + x)/(2x^2 + 5x + 2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 6x^2-x+1/(x^3 + x²+x+1)

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^5+2)/(x^2-1)

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

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x^2+1) + 2x/(x^2+1)^2.

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 5x²-6x+7 /(x − 1) (x² + 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 1/x(x-1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4/(2x^2 -5x -3)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^2)/(x^2 + 2x + 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (2x^2 -18x -12)/x³- 4x

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x²+2x+7/x(x − 1)^2

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^2/(x − 1)² (x + 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x^2 + 4))

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 6x^2-x+1/(x^3 + x²+x+1)

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^5+2)/(x^2-1)

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x^2+1) + 2x/(x^2+1)^2.