Rational Expressions and Equations
Simplifying, combining, and solving with rational expressions
Rational Expressions and Equations
Simplifying, combining, and solving with rational expressions
Math - Grade 9-12
- 1
Simplify the expression (6x)/(9).
Reduce the numerical fraction first.
The expression simplifies to 2x/3. - 2
Simplify the rational expression (x^2 - 9)/(x + 3). State any restriction on x.
Factor the numerator as a difference of squares.
The expression simplifies to x - 3, with the restriction x does not equal -3. - 3
Simplify the rational expression (x^2 + 5x)/(x). State any restriction on x.
The expression simplifies to x + 5, with the restriction x does not equal 0. - 4
Multiply and simplify: (2/x) · (3x/5). State any restriction on x.
Cancel common factors before multiplying.
The product simplifies to 6/5, with the restriction x does not equal 0. - 5
Divide and simplify: (4/x) ÷ (2/x^2). State any restriction on x.
The quotient simplifies to 2x, with the restriction x does not equal 0. - 6
Add and simplify: 3/x + 2/x.
The sum simplifies to 5/x, with the restriction x does not equal 0. - 7
Add and simplify: 1/x + 1/2. State any restriction on x.
Find a common denominator of 2x.
The sum simplifies to (x + 2)/(2x), with the restriction x does not equal 0. - 8
Subtract and simplify: 5/(x + 1) - 2/(x + 1). State any restriction on x.
The difference simplifies to 3/(x + 1), with the restriction x does not equal -1. - 9
Simplify the complex fraction (1/x) / (2/3). State any restriction on x.
Dividing by a fraction means multiplying by its reciprocal.
The expression simplifies to 3/(2x), with the restriction x does not equal 0. - 10
State all values of x that make the expression (x + 4)/(x^2 - 16) undefined.
The expression is undefined when x equals 4 or x equals -4 because those values make the denominator zero. - 11
Solve the rational equation 3/x = 12.
Multiply both sides by x, then divide by 12.
The solution is x = 1/4. - 12
Solve the rational equation x/(x + 2) = 3/4. State any restricted value.
The solution is x = 6, with the restriction x does not equal -2. - 13
Solve the rational equation 2/(x - 1) = 1. State any restricted value.
Multiply both sides by x - 1.
The solution is x = 3, with the restriction x does not equal 1. - 14
Solve the rational equation 1/x + 1/x = 1. State any restricted value.
Combining the left side gives 2/x = 1, so the solution is x = 2, with the restriction x does not equal 0. - 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.
Use area = length × width.
The length is 24/x units, with the restriction x does not equal 0.