Partial Fractions Practice Problems

For the following expression, (7x² + 6x + 23)/(x³ - 18x - 35), perform partial fraction decomposition.

For the following expression, 3/[y(y + 3)], perform partial fraction decomposition, and using the resulting expression, evaluate the following addition:

Using long division, work out the following expression and expand its remainder by doing partial fraction decomposition. 

(s⁴ - 16s² + 8)/(s³ - 4s²)

Using long division, work out the following expression and expand its remainder by doing partial fraction decomposition. 

(y⁵ + 3)/(y² - 9)

Express the following expression in its partial fraction decomposition.

(3c² - 10c + 50)/(c³ - 125)

Express the following expression in its partial fraction decomposition.

(y³ - 11y² + 36y - 31)/(y² - 4y + 5)²

Express the following expression in its partial fraction decomposition.

(y³ + 2y² + y + 12)/(y² + 6)²

Express the following expression in its partial fraction decomposition.

(4x² + 2x - 18)/[(x + 3)(x² + 3)]

Express the following expression in its partial fraction decomposition.

(9y + 1)/[y²(y² + 9)]

Express the following expression in its partial fraction decomposition.

(6y² - 3y + 45)/[(y - 5)(y² + 3y + 5)]

Express the following expression in its partial fraction decomposition.

(9a² - 10a + 57)/(a - 3)(a² + 9)

Express the following expression in its partial fraction decomposition.

4y²/[(y - 2)²(y + 2)]

Express the following expression in its partial fraction decomposition.

(- 2a² + 13a + 36)/[a(a - 6)²]

Express the following expression in its partial fraction decomposition.

(2d² - 23d + 58)/(d - 5)³

Express the following expression in its partial fraction decomposition.

(2d - 13)/(d - 9)²

Express the following expression in its partial fraction decomposition.

(2b² - b - 6)/(b³ - 36b)

Express the following expression in its partial fraction decomposition.

(3a² - 2a - 9)/(a³ - 9a)

Express the following expression in its partial fraction decomposition.

(2y² + 5y - 4)/[y(y - 2)(y + 5)]

Express the following expression in its partial fraction decomposition.

8y/(y² + 4y - 12)

Express the following expression in its partial fraction decomposition.

7/(3y² - y - 4)

Express the following expression in its partial fraction decomposition.

(4y + 16)/(y² + 4y - 12)

Express the following expression in its partial fraction decomposition.

(2y - 9)/(y² - 2y - 35)

Express the following expression in its partial fraction decomposition.

(5x + 19)/(x - 1)(x + 3)

Express the following expression in its partial fraction decomposition.

14/y(y - 7)

Express the following expression in its partial fraction decomposition.

y/(y - 4)(y - 8)

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(3x² - 13x + 25)/(x² + 11)² 

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(3x³ + 2x²)/(x² + 9)² 

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(7x² - 9x + 13)/(x - 4)(x² + 4)

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(8y + 9)/(y + 3)(y - 5)²

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(8x² - 39x - 163)/(x + 4)(x - 7)²

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(2x - 98)/(x - 9)(x + 5)

Find the sum: (2x - 1)/(x² + 9) + 5x/(x² + 9)²

Find the difference: 8/(x - 3) - 5/(x + 6)

For the given rational expression, write in its partial fraction decomposition form.

(2x³ - 4x² - 3x + 1)/(x² + 2x + 3)²

For the given rational expression, write in its partial fraction decomposition form.

(x² + 2x - 10)/(x + 2)(x² + 1)

For the given rational expression, write in its partial fraction decomposition form.

2x/(x + 2)(x² + 4)

For the given rational expression, write in its partial fraction decomposition form.

(x² - 2x + 1)/x(x + 1)(x - 1)

For the given rational expression, write in its partial fraction decomposition form.

x/(x + 5)(x - 4)

What should be multiplied to each side of 9/[7p(5p + 11)] = x/7p + y/(5p + 11), so that the fraction form of the equation is removed? 

What should be multiplied to each side of (8z -1)/(z + 5)(2z² + 7) = A/(z + 5) + (Bz + C)/(2z² + 7), so that the fraction form of the equation is removed? 

What should be multiplied by each side of (5y - 3)/y(9y² + 2)² = A/y + (By + C)/(9y² + 2) + (Dy + E)/(9y² + 2)², so that the fraction form of the equation is removed? 

For the following rational expression, apply partial fraction decomposition.

8/(5P(7P +3))

For the following rational expression, apply partial fraction decomposition.

(8p +4)/((p + 2)(5p -6))

For the following rational expression, apply partial fraction decomposition.

p/(p² -4p -21)

Decompose the given rational function in partial fractions. 

17/t(t +1)

Decompose the given rational function in partial fractions. 

(3p² +4p +28)/[p(p +2)(p -2)]

Decompose the given rational function in partial fractions. 

(3t +2)/(t +5)³

For the following rational expression, apply partial fraction decomposition. 

(t²)/(t² + 6t +9)

For the following rational expression, apply partial fraction decomposition. 

(t³ +7)/(4t³ -t)

For the following rational expression, apply partial fraction decomposition.

-9/[t²(t² +7)]

For the following rational expression, apply partial fraction decomposition.

(5t - 2)/((t +1)(3t² +3))

For the following rational expression, apply partial fraction decomposition.

1/t(4t +1)(2t² +1)

For the following rational expression, apply partial fraction decomposition. 

(3x⁵-19x⁴+37x³-21x²+x+1)/(3x²-16x+21)

Decompose the given rational function in partial fractions. 

(6t -7)/t(3t² +2)²

Decompose the given rational function in partial fractions. 

(-7x⁴-28x²+5x+7)/(x + 7)(x² +2)²

Decompose the given rational function in partial fractions. 

(3t²)/7(t⁴ - 1)

Decompose the given rational function in partial fractions. 

(3t²-t+3)/(t³-2t²-3t)

Decompose the given rational function in partial fractions. 

8/(5x²-12x+7)

For the following rational expression, apply partial fraction decomposition.

(7 -3x)/[(x² +7)(x -3)]