What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0?
Choose the most appropriate option
A) -2
B) 10
C) -1
D) 3
E) 0
Let us factorize the denominator and rewrite the expression as (xâˆ’3)/((xâˆ’10)(x+2))&gt; 0   Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.   The values that are relevant to us are x = 3, x = 10 and x = -2.   Let us arrange these values in ascending order: -2, 3 and 10.   The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.   Interval 1: x &lt; -2.   Pick a value in that range and check whether the inequality holds good.   Let us take x = -10. When x = -10, (xâˆ’3)/((xâˆ’10)(x+2))&lt; 0; the inequality DOES NOT hold good in this interval.   Interval 2: -2 &lt; x &lt; 3.   Let us take x = 0. When x = 0, (xâˆ’3)/((xâˆ’10)(x+2)) = (0âˆ’3)/((0âˆ’10)(0+2)) &gt; 0; the inequality holds good in this interval.   The least integer value that x can take if x &gt; -2 is x = -1.   ANSWER : -1.
<result>C</result>
What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0?