HOW TO FIND THE EXCLUDED VALUE OF A RATIONAL EXPRESSION

How to Find the Excluded Value of a Rational Expression ?

A value that makes a rational expression (in its lowest form) undefined is called an Excluded value.

To find excluded value for a given rational expression in its lowest form, say p (x)/q (x), consider the denominator q(x) = 0.

How to Find the Excluded Value of a Rational Expression - Questions

Question 1 :

Find the excluded values, if any of the following expressions.

(i)  y/(y2 - 25)

Solution :

=  y/(y2 - 25)

y2 - 25  =  y2 - 52

  =  (y - 5)(y + 5)

=  y/(y + 5) (y - 5)

By equating the denominator equal to zero, we get y + 5 = 0 and y - 5  =  0.

y + 5 = 0  and  y - 5  =  0

 y = -5 and y = 5

Hence the excluded values are -5 and 5.

(ii)  t/(t2 - 5t + 6)  

Solution :

=  t/(t2 - 5t + 6)  

 t2 - 5t + 6  =  (t - 2)(t - 3)

=  t/(t - 2)(t - 3)

By equating the denominator equal to zero, we get t- 2  = 0 and t - 3  =  0

t - 2 = 0  and  t - 3  =  0

 y = 2 and y = 3

Hence the excluded values are 2 and 3.

(ii)  (x2 + 6x + 8)/(x2 + x - 2) 

Solution :

=  (x2 + 6x + 8)/(x2 + x - 2) 

x2 + 6x + 8  =  (x + 2)(x + 4)

(x2 + x - 2)  =  (x + 2)(x - 1)

=  (x + 2)(x + 4)/(x + 2)(x - 1)

=  (x + 4)/(x - 1)

By equating the denominator equal to zero, we get x - 1  =  0

Hence the excluded value is 1.

(iv)  (x3 - 27) / (x3 + x2 - 6x)

Solution :

x3 - 27  =  x3 - 3

  =   (x - 3)(x2 + x(3) + 32)

  =   (x - 3)(x2 + 3x + 9)

x3 + x2 - 6x  =  x(x2 + x - 6)

 =  x(x + 3)(x - 2)

 =  (x - 3)(x2 - 3x + 9) / x(x + 3)(x - 2)

By equating the denominator equal to zero, we get x = 0, x + 3 = 0 and x - 2 = 0

Hence the excluded value is 0, 2 and 3.

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