If f(x) = x⁴ − x³ + x² and g(x) = −x², Where x ≠ 0, What is (f/g)(x)?

We will use the concept of functions to solve this.

Answer:  If f(x) = x^{4} − x^{3} + x^{2} and g(x) = −x^{2}, then (f/g)(x) = x − x^{2} − 1 

Let's solve this step by step.

Explanation:

Given that, f(x) = x⁴ − x³ + x² and g(x) = −x² 

We know from function that: (f/g)(x) = f(x) / g(x)

(f/g)(x) = (x⁴ − x³ + x²) / (−x²)

= x²(x² − x + 1) / (−x²)

= -(x² − x + 1)

= x − x² − 1 

Hence, If f(x) = x⁴ − x³ + x² and g(x) = −x², then (f/g)(x) = x − x² − 1