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WEEK 4
TOPIC: ALGEBRAIC FRACTIONS
CONTENT:
- Simplification of fractions.
- Operation in algebraic fractions.
- Equation involving fraction.
- Substitution in fractions.
- Simultaneous equation involving fractions.
- Undefined value of a fraction.
SIMPLIFICATION OF FRACTIONS
An algebraic fraction is a part of a whole, represented mathematically by a pair of algebraic terms. The upper part is called the numerator while the lower part the denominator. To simplify algebraic fractions, we need to factorize both the numerator and the denominator.
Examples:
- Reduce the following to their lowest term
(〖3x〗^2+9x^2 y^2)/(3x^2 y)
(x^2-y^2+3x+3y)/(x-y+3)
(x^2-9)/(x^2+x-6)
(5xy-10x+y-2)/(8-〖2y〗^2 )
Solution:
(〖3x〗^2+9x^2 y^2)/(3x^2 y)=(〖3x〗^2 (1+〖3y〗^2 ))/(〖3x〗^2×y)
Cancel the common factors i.e.〖3x〗^2
.∴ Ans=(1+〖3y〗^2)/y
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