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Objectives
Revision On:• Simplify of Algebraic Fraction
• Perform Operations on Algebraic Fraction
• Solve Equations Involving Algebraic Fraction
• Make Substitution in Algebraic Fraction
• Solve Simultaneous Equations Involving Algebraic Fraction
• Undefined value of an Algebraic Fraction
• Represent Algebraic Fractions Graphically.
Simplification of Algebraic Fractions
Like in common fractions, algebraic fractions can be reduced to their lowest form, by dividing numerators and denominators by their common factor(s).
Example 1
Reduce to its lowest form.
Solution
=
4)
= b(b – 4)
=
• Example 2
Simplify
Solution
Factorize numerator =
(x – 4)(x – 4)
Factorize denominator =
(x - 4)(x – 3)
= =
Operations on Algebraic Fractions
Example 3
Simplify
Solution
LCM of (m+2n) and (m – 3n) is
(m+2n)(m – 3n)
=
=
=
Equations Involving Algebraic Fractions
Example 4
Solve the equation
Solution
Multiply each by LCM of the denominators
(2k+1)(2k-3)(k-1)
(2k+1)(2k-3)(k-1)+ (2k+1)(2k-3)(k-1)=0
= (2k-3)(k-1) + (2k+1)(k-1) (2k+1)(2k-3)
K = 2 ½
Solve Simultaneous Equations Involving Algebraic Fraction
STEPS:
1.Find the LCM of the denominators of each equation.
2.Multiply through by the LCM to clear the fractions.
3.Solve both resulting equations simultaneously
• Example 5
Solve the following pair of equations.
The LCM is 8. Multiply through by 8.
4 = 2
The LCM is 15. Multiply through by 15.
9 = 2
After clearing the fractions, solve simultaneously
= 2 , = 2
4 = 2 __________ (1)
9 = 2 ___________ (2)
• Example 6
Solve
LCM of denominator of first equation is
LCM of denominator of second equation is
Multiply both side of first equation by x
Multiply both side of second equation by 2x1 + 2y = 5x
3 + 4y = 7x
x
2x
1 + 2y = 5x ________ (1)
3 + 4y = 7x ________ (2)
After clearing the fractions, solve simultaneously
X =
Read Up
• Make Substitution in Algebraic Fraction
• Undefined value of an Algebraic Fraction
Reference: MAN Mathematics SS 2
Undefined Value of Algebraic Fraction
• For algebraic fraction to be undefined, the following conditions must apply:
1.The numerator and denominator must have no common factor(s)
2.The denominator must be equal to zero.
• Example 7
Find the value of x for which is undefined.
Solution
Since the numerator and denominator doesn’t have any common factor, equate the denominator to zero.
= 0
Solve for x,
X= - 1/5
Example 8
Find the value of x for which is undefined.
Solution
Since there is a common factor, factorize first.
The equate the denominator to zero and solve for x:
Since there is no x in the denominator, then x has no value.
References
• https://www.youtube.com/watch?v=EPM5XEXKa_Y
• https://www.youtube.com/watch?v=2N62v_63SBo
• https://www.youtube.com/watch?v=vA-55wZtLeE
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