Rational Expressions and Equations Worksheet

Question 1

Simplify the expression (6x)/(9).

Accepted Answer

The expression simplifies to 2x/3.

Question 2

Simplify the rational expression (x^2 - 9)/(x + 3). State any restriction on x.

Accepted Answer

The expression simplifies to x - 3, with the restriction x does not equal -3.

Question 3

Simplify the rational expression (x^2 + 5x)/(x). State any restriction on x.

Accepted Answer

The expression simplifies to x + 5, with the restriction x does not equal 0.

Question 4

Multiply and simplify: (2/x) · (3x/5). State any restriction on x.

Accepted Answer

The product simplifies to 6/5, with the restriction x does not equal 0.

Question 5

Divide and simplify: (4/x) ÷ (2/x^2). State any restriction on x.

Accepted Answer

The quotient simplifies to 2x, with the restriction x does not equal 0.

Question 6

Add and simplify: 3/x + 2/x.

Accepted Answer

The sum simplifies to 5/x, with the restriction x does not equal 0.

Question 7

Add and simplify: 1/x + 1/2. State any restriction on x.

Accepted Answer

The sum simplifies to (x + 2)/(2x), with the restriction x does not equal 0.

Question 8

Subtract and simplify: 5/(x + 1) - 2/(x + 1). State any restriction on x.

Accepted Answer

The difference simplifies to 3/(x + 1), with the restriction x does not equal -1.

Question 9

Simplify the complex fraction (1/x) / (2/3). State any restriction on x.

Accepted Answer

The expression simplifies to 3/(2x), with the restriction x does not equal 0.

Question 10

State all values of x that make the expression (x + 4)/(x^2 - 16) undefined.

Accepted Answer

The expression is undefined when x equals 4 or x equals -4 because those values make the denominator zero.

Question 11

Solve the rational equation 3/x = 12.

Accepted Answer

The solution is x = 1/4.

Question 12

Solve the rational equation x/(x + 2) = 3/4. State any restricted value.

Accepted Answer

The solution is x = 6, with the restriction x does not equal -2.

Question 13

Solve the rational equation 2/(x - 1) = 1. State any restricted value.

Accepted Answer

The solution is x = 3, with the restriction x does not equal 1.

Question 14

Solve the rational equation 1/x + 1/x = 1. State any restricted value.

Accepted Answer

Combining the left side gives 2/x = 1, so the solution is x = 2, with the restriction x does not equal 0.

Question 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.

Accepted Answer

The length is 24/x units, with the restriction x does not equal 0.

Rational Expressions and Equations

Rational Expressions and Equations

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