Operations on Rational Expressions
Operations on Rational Expressions1Rational expressions are
fractions in which the numerator and denominator are polynomials
and the denominator does not equal zero. Example: Simplify
, x 3 0, x 321. Factor the numerator and denominator of each
fraction.2. Multiply the numerators and denominators of each
fraction.4. Write the answer in simplest form.3. Divide by the
common factors.To multiply rational expressions:
3
Factor the numerator and denominator of each fraction.Divide by
common factors.Write the answer in simplest form.
Multiply Example:
Multiply.4
1. Multiply the dividend by the reciprocal of the divisor. The
reciprocal of is .2. Multiply the numerators. Then multiply the
denominators.4. Write the answer in simplest form.3. Divide by the
common factors.To divide rational expressions:
5
Example: Divide
Multiply by the reciprocal of the divisor.Factor and
multiply.Divide by the common factors.Simplest form.
6The least common multiple (LCM) of two or more numbers is the
least number that contains the prime factorization of each
number.Examples: 1. Find the LCM of 10 and 4.2. Find the LCM of 4x2
+ 4x and x2 + 2x + 1.4x2 + 4x = (4x)(x +1) = 2 2 x (x + 1) x2 + 2x
+ 1 = (x +1)(x +1)LCM = 2 2 x (x +1)(x +1)factors of 4x2 + 4x
factors of x2 + 2x + 1 10 = (5 2) LCM = 2 2 5factors of 10factors
of 4 4 = (2 2)= 4x3 + 8x2 + 4x = 207LCMFractions can be expressed
in terms of the least common multiple of their
denominators.Example: Write the fractions and in terms of the LCM
of the denominators.
The LCM of the denominators is 12x2(x 2).
8If necessary, rewrite the fractions with a common
denominator.To add rational expressions:
To subtract rational expressions:2. Add the numerators of each
fraction. **Denominator stays the same!If necessary, rewrite the
fractions with a common denominator.2. Subtract the numerators of
each fraction. **Denominator stays the same!
9Example: Add
Example: Subtract
10Two rational expressions with different denominators can be
added or subtracted after they are rewritten with a common
denominator.Example: Add
11Example: Subtract
Add numerators.Factor.Divide.Simplest form.12
