ALGEBRAIC FRACTION –
Fraction in which the numerator or denominator or both are algebraic expressions are called algebraic fraction.
x 2 x - 6
Example.) -------, --------, and ----------- are algebraic fractions.
2 x² + 3 x² + 3x + 2
Algebraic fractions can be reduced, added, subtracted, multiplied and divided according to the same rules that govern arithmetic fractions.
Reduction To Lowest Terms –
When the numerator and denominator of an algebraic fractions do not have any common factor except 1, the algebraic fraction is said to be expressed in the lowest terms.
To reduce an algebraic fraction to the lowest terms, take the following steps.
Step.1) Factorize the numerator and the denominator.
Step.2) Cancel the factors that are common to the numerator and the denominator.
15a⁴
Example.1) -----------
35a⁵
3 X 5 X a X a X a X a 3
= ------------------------- = --------- = 3/7a
5 X 7 X a X a X a X a X a 7 X a
15a⁴ 15 a⁴
Alternatively, --------- = -------- X --------
35a⁵ 35 a⁵
3 1 3
= ------- X -------- = --------- (Ans.)
7 a⁵⁻⁴ 7a
9 aᶟb⁵c⁶
Example.2) -------------
12 a⁶b⁴c²
3 X 3 X a X a X a X b X b X b X b X b X c X c X c X c X c X c
= -----------------------------------------------------------
3 X 4 X a X a X a X a X a X a X b X b X b X b X c X c
3bc⁴
= ---------- (Ans.)
4aᶟ
Alternatively,
9 aᶟb⁵c⁶
----------------
12 a⁶b⁴c²
9 aᶟ b⁵ c⁶
= ---------- X ---------- X ---------- X ----------
12 a⁶ b⁴ c²
3 1
= -------- X --------- X b⁵⁻⁴ X c⁶⁻²
4 a⁶⁻ᶟ
3bc⁴
= ---------- (Ans.)
4aᶟ
125a⁴b²c⁵
Example.3) ----------------
175a⁴b⁵c⁴
5 X 5 X 5 X a X a X a X a X b X b X c X c X c X c X c
= ---------------------------------------------------------
5 X 5 X 7 X a X a X a X a X b X b X b X b X b X c X c X c X c
5c
= ---------- (Ans.)
7bᶟ
Alternatively,
125a⁴b²c⁵ 125 a⁴ b² c⁵
------------ = -------- X -------- X -------- X --------
175a⁴b⁵c⁴ 175 a⁴ b⁵ c⁴
5 X a⁰ X c⁵⁻⁴
= -----------------
7 X b⁵⁻²
5 X 1 X c¹ 5c
= ---------------- = --------- (Ans.)
7 X bᶟ 7bᶟ