**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.

**Question 1 :**

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

(i) y/(y^{2} - 25)

**Solution :**

= y/(y^{2} - 25)

y^{2} - 25 = y^{2} - 5^{2}

= (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/(t^{2} - 5t + 6)

**Solution :**

= t/(t^{2} - 5t + 6)

t^{2} - 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) (x^{2} + 6x + 8)/(x^{2} + x - 2)

**Solution :**

= (x^{2} + 6x + 8)/(x^{2} + x - 2)

x^{2} + 6x + 8 = (x + 2)(x + 4)

(x^{2} + 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) (x^{3} - 27) / (x^{3} + x^{2} - 6x)

Solution :

x^{3} - 27 = x^{3} - 3^{3 }

= (x - 3)(x^{2} + x(3) + 3^{2})

= (x - 3)(x^{2} + 3x + 9)

x^{3} + x^{2} - 6x = x(x^{2} + x - 6)

= x(x + 3)(x - 2)

= (x - 3)(x^{2} - 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.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Excluded Value of a Rational Expression".

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