Page 141 - Algebra

7.3. Mixed and Complex Rational Expressions
A mixed rational expression is a sum or difference of a polynomial and a rational expression. For example,
2𝑥 𝑥+1
is a mixed expression because it is comprised of the difference between a monomial and a
7 –
rational expression.
When a rational expression has more than one fraction either in the numerator or the denominator, the expression is called a complex expression.
For example,
𝑥+1
𝑥 is a complex expression. 𝑥−1
𝑥
In other words,
𝑝 ÷ 𝑟 = 𝑝 × 𝑠 = 𝑝𝑠
𝑞 𝑠 𝑞 𝑟 𝑞𝑟 Here, q ≠ 0 and r ≠ 0
Worked Example
𝑥−3
Simplify 𝑥2−16 𝑥2−9
𝑥+4
Solution:
𝑥−3 = 𝑥2−16 𝑥2 −9
𝑥+4
= 𝑥−3 ÷𝑥2−9 𝑥2−16 𝑥+4
= 𝑥−3 × 𝑥+4 𝑥2−16 𝑥2−9
= 𝑥−3 × 𝑥+4 (𝑥−4)(𝑥+4) (𝑥−3)(𝑥+3)
=1 (𝑥−4)(𝑥+3)
Page 140 of 177
Algebra I & II