Vocabulary
Simplified Form of a Rational Expression- A rational expression in which the numerator and denominator have no common factors other than ±1
Reciprocal- a number if multiplied with another equals 1. 1/8 is the reciprocal of 8.
Reciprocal- a number if multiplied with another equals 1. 1/8 is the reciprocal of 8.
Essential Information
A rational expression is in simplified form if its numerator and denominator have no common factors (other than ±1).
Simplifying Rational Expressions
Let a, b, and c be expressions with b≠ 0 and c≠0. Then...
Simplifying Rational Expressions
Let a, b, and c be expressions with b≠ 0 and c≠0. Then...
Simplifying a rational expression usually requires 2 steps:
Common factors can be canceled out, yet like terms cannot.
- Factor the numerator and denominator
- Divide out any factors that are common to both the numerator and denominator
Common factors can be canceled out, yet like terms cannot.
Multiplying Rational Expressions
The rule for multiplying rational expressions is the same rule for multiplying numerical fractions: multiply numerators, multiply denominators, and write the new fraction in simplified form.
The rule for multiplying rational expressions is the same rule for multiplying numerical fractions: multiply numerators, multiply denominators, and write the new fraction in simplified form.
Dividing Rational Expressions
To divide one rational expression by another, multiply the first rational expression by the reciprocal of the second rational expression. Keep Change Flip
To divide one rational expression by another, multiply the first rational expression by the reciprocal of the second rational expression. Keep Change Flip