Practice simplifying rational expressions, finding restrictions, performing operations, and solving rational equations.
Read each problem carefully. Simplify all answers when possible, and state any values that make an expression undefined.
Simplifying, combining, and solving with rational expressions
Math - Grade 9-12
- 1
Simplify the expression (6x)/(9).
- 2
Simplify the rational expression (x^2 - 9)/(x + 3). State any restriction on x.
- 3
Simplify the rational expression (x^2 + 5x)/(x). State any restriction on x.
- 4
Multiply and simplify: (2/x) · (3x/5). State any restriction on x.
- 5
Divide and simplify: (4/x) ÷ (2/x^2). State any restriction on x.
- 6
Add and simplify: 3/x + 2/x.
- 7
Add and simplify: 1/x + 1/2. State any restriction on x.
- 8
Subtract and simplify: 5/(x + 1) - 2/(x + 1). State any restriction on x.
- 9
Simplify the complex fraction (1/x) / (2/3). State any restriction on x.
- 10
State all values of x that make the expression (x + 4)/(x^2 - 16) undefined.
- 11
Solve the rational equation 3/x = 12.
- 12
Solve the rational equation x/(x + 2) = 3/4. State any restricted value.
- 13
Solve the rational equation 2/(x - 1) = 1. State any restricted value.
- 14
Solve the rational equation 1/x + 1/x = 1. State any restricted value.
- 15
A rectangle has area 24 square units and width x units. Write and simplify a rational expression for the length of the rectangle in terms of x. State any restriction on x.