Exams › JEE Advanced › Maths

Solve for real x: 1/(x + 1) + 2/(x + 2) > 3/(x + 3).

1. x in (-infinity, -3) U (-2, -3/2) U (-1, infinity)
2. x in (-3, -2) U (-3/2, -1)
3. x in (-infinity, -3) U (-1, infinity)
4. x in (-2, infinity)

Correct answer: x in (-infinity, -3) U (-2, -3/2) U (-1, infinity)

Solution

Move the right side over, combine to a single fraction, find its numerator roots and the excluded points, then use a sign chart across the critical values.

Related JEE Advanced Maths questions

• Solve the inequality over the real numbers: ((x - 1)(x + 2)²) / (-1 - x) < 0.
• Solve the inequality over the real numbers: ((x - 1)² * (x + 1)³) / (x⁴ * (x - 2)) <= 0.
• Solve the inequality over the reals: ((2 - x²)*(x - 3)³) / ((x + 1)*(x² - 3x - 4)) >= 0.
• Solve the inequality over the real numbers: x/(x + 1) > 2. Which option is the solution set?
• For f(x) = (x³ + 4x² - 11x - 30)/(x² - 6x - 7), determine the set of x for which f(x) > 0.
• Solve over the real numbers: (x - 1)² (x + 1)³ (x - 4) < 0. Give the solution set.

⚔️ Practice JEE Advanced Maths free + battle 1v1 →