To simplify the expression, let's first factorize the denominator, which is a quadratic equation:
(x^2 - 2) * (x^2 - 5x + 4)= (x - √2)(x + √2)(x - 1)(x - 4)
Now, we can rewrite the expression with the factored denominator:
We have the expression x^5 - 4x^4 - 4x + 16 / ((x - √2)(x + √2)(x - 1)(x - 4))
To simplify further, you can divide x^5 - 4x^4 - 4x + 16 by each of the factors in the denominator separately:
x^5 = (x^5 - 8x^4 + 4x^4) = 8x^4 - 4x^4 = 4x^4-4x^4 = (-4x^4 + 8x^3 - 4x^3) = 8x^3 - 4x^3 = 4x^3-4x = (-4x + 8) = 8, so -4x = 8
Therefore, the simplified expression is 4x^4 + 4x^3 + 8/(x - √2)(x + √2)(x - 1)(x - 4)
To simplify the expression, let's first factorize the denominator, which is a quadratic equation:
(x^2 - 2) * (x^2 - 5x + 4)
= (x - √2)(x + √2)(x - 1)(x - 4)
Now, we can rewrite the expression with the factored denominator:
We have the expression x^5 - 4x^4 - 4x + 16 / ((x - √2)(x + √2)(x - 1)(x - 4))
To simplify further, you can divide x^5 - 4x^4 - 4x + 16 by each of the factors in the denominator separately:
x^5 = (x^5 - 8x^4 + 4x^4) = 8x^4 - 4x^4 = 4x^4
-4x^4 = (-4x^4 + 8x^3 - 4x^3) = 8x^3 - 4x^3 = 4x^3
-4x = (-4x + 8) = 8, so -4x = 8
Therefore, the simplified expression is 4x^4 + 4x^3 + 8/(x - √2)(x + √2)(x - 1)(x - 4)