Algebraic Fractions

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 =

Classwork

Solve the following simultaneous equations

1. 2

2.

ans: x=3, y=-1

ans: x= , y=

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.

Classwork

• Find the value of x for which the following algebraic fractions are undefined.

1.2.

Correction

10 – 2x = 0

2x = 10

X = 5

6x = 0X = 0

3. Factorizing (x+2) (x -7) =X -7 = 0X =7

Graphical Interpretation of Undefined 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

Email: hammedalao@gmaill.com