Adding and Subtracting Rational Expressions

Adding Monomials

100

1/x + 2/x

3/x

200

2/4x+3/6x

1/x

300

x+1/18 + x-1/45

7x +3/90

400

3/ab+5/4b

12+5a/4ab

Subtracting Monomials

100

x/3-x/7

4x/21

200

4a/b-3a/2b

5a/2b

300

7bc/4cb-8b/3bc

21c-32/12c

400

11c²/2b-3c²/8b²

44bc²-3c²/8b²

Adding Polynomials

100

2/x-3+7/2x-6

11/2x-6

200

2x/x²-4 + 3/x-2

5x+6/(x+2)(x-2)

300

12/x+8+3/x-9

15x-84/(x+8)(x-9)

400

4x²-9/x²-1 + 2x-1/x+1

6x²-3x-8/(x+1)(x-1)

Subtracting Polynomials

100

2x/x+1 - x/x+1

x/x+1

200

x²-4/x-2 - x+1/x+2

x²+3x+3/x+2

300

2x/x-1-4x/x+1

-2x²+6x/x²-1

400

a+1/5-2a - a-4/2a-5

2a-3/-(2a-5) or 3-2a/2a-5

Word Problems

100

The length of a rectangle is represented by 2x/3 meters, and the width is represented by x/2 meters. What is the expression for the total perimeter of the rectangle?

7x/3

200

Lily is combining two chemical solutions. The first, represented by x+3/x+5, and the second by  x+2/x²+3x-10. What is the simplified expression when these solutions are mixed together?

x²+2x-4/(x+5)(x-2)

300

A farmer is dividing a field into two sections. His whole field requires 4xy-2x/3xy fertilizer and one portion of the field requires 3y-1/2xy fertilizer. What amount of fertilizer does the other portion require?

8xy-4x-9y+3/6xy

400

If your current mark is 2b+3/4b-1 and Mr. Welch takes off b+6/1-4b marks because he doesn't like you. What is your final mark?

3b+9/4b-1 or 3(b+3)/4b-1