SIMPLIFYING RATIONAL EXPRESSIONS WORKSHEET

Simplify the following rational expressions.

Problem 1 :

(2x + 6) / (4x - 12)              Solution

Problem 2 :

(x² + 9x + 20) / (2x + 8)       Solution

Problem 3 :

(6x + 24)/(x² +7x + 12)       Solution

Problem 4 :

(3x + 18)/(x²+6x)       Solution

Problem 5 :

(3x - 12)/(3x² - 12x)       Solution

Problem 6 :

(x² - 5x + 6)/(x² + 2x - 15)       Solution

Problem 7 :

 (4x + 4)/(x² + 4x + 3)       Solution

Problem 8 :

(x² - x - 12)/(x² - 2x - 8)       Solution

Problem 9 :

(x² - 5x + 4)/(x² - 4x)       Solution

Problem 10 :

(x² - x - 30)/(x² - 12x + 36)       Solution

Write and simplify a rational expression for the ratio of the perimeter of the figure to its area.

Problem 11 :

Solution

Problem 12 :

Solution

Problem 12 :

Solution

Problem 1 :

p² + 14p + 48

Solution

Problem 2 :

n² + 10n + 16

Solution

Problem 3 :

p² + 14p + 40

Solution

Problem 4 :

r² + 9r + 18

Solution

Problem 5 :

p² - 8p + 7

Solution

Problem 6 :

b² - 9b + 14

Solution

Problem 7 :

b² - 8b + 15

Solution

Problem 8 :

m² - 16m + 63

Solution

Problem 9 :

k² - 4k – 60

Solution

Problem 10 :

m² + m – 6

Solution

Problem 11 :

p² - 2p – 15

Solution

Problem 12 :

r² + r – 20

Solution

Problem 13 :

The area (in square centimeters) of a square coaster can be represented by

d² + 8d + 16

a. Write an expression that represents the side length of the coaster.

b. Write an expression for the perimeter of the coaster.

Solution

Problem 14 :

The polynomial represents the area (in square feet) of the square playground.

a. Write a polynomial that represents the side length of the playground.

b. Write an expression for the perimeter of the playground.

Solution

Problem 15 :

Tell whether the polynomial can be factored. If not, change the constant term so that the polynomial is a perfect square trinomial.

a. w² + 18w + 84     Solution

b. y² − 10y + 23     Solution

Problem 16 :

The width of a calculator can be represented by (3x + 1) inches. The length of the calculator is twice the width. Write a polynomial that represents the area of the calculator.

Solution

Factor the following quadratic polynomial :

Problem 1 :

7m² + 6m - 1                  Solution

Problem 2 :

3k² - 10k + 7            Solution

Problem 3 :

5x² - 36x - 81            Solution

Problem 4 :

2x² - 9x - 81            Solution

Problem 5 :

3n² - 16n + 20            Solution

Problem 6 :

2r² + 7r - 30            Solution

Problem 7 :

5k² + 8k + 80            Solution

Problem 8 :

5x² - 14x + 8            Solution

Problem 9 :

7p² - 20p + 12            Solution

Problem 10 :

7x² - 26x - 45            Solution

Problem 11 :

3v² + 14v - 49            Solution

Problem 12 :

 5p² - 52p + 20            Solution 

Problem 13 :

The volume (in cubic feet) of a room in the shape of a rectangular prism is represented by 12z³ − 27z. Find expressions that could represent the dimensions of the room.

Solution

Problem 14 :

Factor

(a) 3x³ + 6x² − 18x

(b) 7x⁴ − 28x²

Solution

Problem 15 :

Can you use the perfect square trinomial pattern to factor y² + 16y + 64? Explain.

Solution

Problem 16 :

Which polynomial does not belong with the other three? Explain your reasoning.

a)  g² − 6g + 9      b)  n² − 4     c)  r² + 12r + 36     d)  g² + 25

Solution