The question is for finding the solution of a inequality. We need to solve the inequality which is in the form of fraction. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 17: Solve :\\frac{(x – 4) (x+3)}{(x + 4) ( x +5)}\\) > 0?

- x ∊ (-∞,-5) ∪ (-4 , -3) ∪ (4, ∞)
- x ∊ (-∞,-5) ∪ (4, ∞)
- x ∊ (-4,-3) ∪ (4, ∞)
- x ∊ (-5,-3] ∪ [4, ∞)

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

\\frac{(x – 4) (x+3)}{(x + 4) ( x + 5)}\\) > 0

Consider this as \\frac{a * b}{c * d}\\) > 0

Clearly, here a < b < c < d

Therefore for \\frac{a * b}{c * d}\\) to be positive (that is, > 0),

all of a,b,c,d must be -ve or

all of a,b,c,d must be positive or

any two of a,b,c,d must be negative and other two positive. Since a < b < c < d, a and b must be negative

So, we have 3 cases for \\frac{(x – 4) (x+3)}{(x + 4) ( x + 5)}\\) > 0

Case i) (x – 4) , (x+3) , (x + 4) , ( x + 5) must be positive.

To satisfy this the smallest number needs to be positive.

(x – 4) > 0 ; **x >4**

Case ii) (x – 4) , (x+3) , (x + 4) , ( x + 5) must be negative.

To satisfy this the largest number needs to be negative.

(x + 5) < 0 ; **x <-5**

Case iii) (x – 4) , (x+3) must be negative and (x + 4) , ( x + 5) must be positive.

(x – 4) , (x+3) must be negative

To satisfy this the largest number needs to be negative.

(x + 3) < 0 ; **x <-3**

(x + 4) , ( x + 5) must be positive.

To satisfy this the smallest number needs to be positive.

(x + 4) > 0 ; **x >-4**

Combining these two, -4 < x < -3

Combining all x < -5, -4 < x < -3, x > 4,

Hence range is (-∞,-5) ∪ (-4 , -3) ∪ (4, ∞)

The question is **"Solve :\\frac{(x – 4) (x + 3)}{(x + 4) ( x + 5)}\\) > 0?"**

Choice A is the correct answer.

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com