Page 139 - Algebra

7. RationalExpressions
7.1. Algebraic fraction
You already know that a fraction is a quotient of a number divided by a nonzero number. It’s always of the form 𝑝, where q ≠ 0. Similarly, an algebraic fraction is a quotient of two algebraic expressions. An
𝑞
algebraic fraction holds only for those values of the variables for which the denominator is not zero. For example,
𝑥+5 is an algebraic fraction, which holds true only when x ≠3 because the denominator will become zero. 𝑥−3
REMEMBER:
• You can add or subtract algebraic fractions only when the denominator is the same.
• When multiplying two algebraic fractions, multiply the numerator with the numerator of the
other, and do the same with the denominator.
• When dividing two algebraic fractions, multiply by the reciprocal or the inverse of the other 𝑝𝑞
number. For example, a reciprocal of 𝑞 is 𝑝.
And,𝑝 ÷𝑟 =𝑝 ×𝑠 𝑞𝑠𝑞𝑟
Worked Example
For what value of x, the expression 14+𝑥 is not defined? −𝑥−8
Solution:
A fraction is not defined when the denominator becomes zero.
Here, x≠8
–x – 8 ≠ 0
–x ≠ – 8
Worked Example
If x = 7, find the value of the following expression
Solution:
Put x = 7, in the above equation.
−𝑥+6
=
72−3(7)+6
=
49−21+6
−7+6
−1
= −34
𝑥2−3𝑥+6
Page 138 of 177
Algebra I & II