Question

Solve the inequality

Answer 1

Answer:

See answer in above picture

Answer 2

The final answer is $x\in (-4,2) \ and (3, \infty)$

Step-by-step explanation:

$\ Given \ value:\\\\\frac{x^4(x+1)^2(x-2)}{(x-3)^3(x+4)} > 0\\\\\ Solution:\\\\\frac{x^4(x+1)^2(x-2)}{(x-3)^3(x+4)} > 0 \\\\\rightarrow \frac{x^4(x^2+1+2x)(x-2)}{(x^3-3^3-3\cdot x\cdot3(x-3)(x+4)} > 0\\\\\rightarrow \frac{x^4(x^3-2x^2+x-2+2x^2-4x)}{(x^3-3^3-9x(x-3)(x+4)} > 0\\\\\rightarrow \frac{x^4(x^3-2-3x)}{(x^3-27-9x^2+27x)(x+4)} > 0\\\\\rightarrow \frac{x^4(x^3-2-3x)}{(x^4+4x^3-27x-108-9x^3-36x^2+27x^2+108x)} > 0\\\\ \rightarrow \frac{(x^7-2x^4-3x^5)}{(x^4-5x^3-9x^2+81x-108)} > 0$

$x\in (-4,2) \ and (3, \infty)$

Learn more:

• Simplify: https://brainly.in/question/8913062