Question

У= (0,25х в квадрате - х)|х| / х-4

Answer 1

Пошаговое объяснение:

у= (0,25х² - х)|х| / (х-4)

y=0,25x(x-4)|x| / (x-4) = 0,25x|x|

Answer 2

To simplify the given expression, let's break it down step by step:

1. Simplify the expression inside the absolute value |x|:

   • For x ≥ 0, |x| = x
   • For x < 0, |x| = -x

2. Divide the expression into two cases: x ≥ 0 and x < 0.

Case 1: x ≥ 0

• Inside the absolute value, |x| = x
• So the expression becomes: (0.25x^2 - x) * x / (x - 4)
• Combine like terms in the numerator: (0.25x^3 - x^2) / (x - 4)

Case 2: x < 0

• Inside the absolute value, |x| = -x
• So the expression becomes: (0.25x^2 - x) * (-x) / (x - 4)
• Distribute the negative sign: (-0.25x^3 + x^2) / (x - 4)

Therefore, the simplified expression for the given function is: (0.25x^3 - x^2) / (x - 4), for x ≥ 0 (-0.25x^3 + x^2) / (x - 4), for x < 0