To solve this equation, we can first combine the terms on the right side:
x^3 - 3x^2 - 4 = 1/(x-1) + 5
Next, let's multiply both sides of the equation by (x-1) to eliminate the fraction:
(x-1)(x^3 - 3x^2 - 4) = (x-1)(1/(x-1) + 5)
Expanding both sides:
x^4 - 4x^3 + 3x^2 - x^3 + 3x^2 + 4x - 4 = 1 + 5(x-1)
Combining like terms:
x^4 - 5x^3 + 6x^2 + 4x - 4 = 1 + 5x - 5
Simplifying:
x^4 - 5x^3 + 6x^2 + 4x - 4 = 5x - 4
Now, let's rearrange the equation to have all terms on one side:
x^4 - 5x^3 + 6x^2 + 4x - 5x + 4 - 4 = 0
Simplifying further:
x^4 - 5x^3 + 6x^2 - x^2 + 3x - 4 = 0
Now, let's factor the equation using grouping:
(x^4 - 5x^3) + (6x^2 - x^2) + (3x - 4) = 0
x^3(x - 5) + x^2(6 - 1) + (3x - 4) = 0
x^3(x - 5) + x^2(5) + (3x - 4) = 0
Factoring out common terms:
(x - 5)(x^3 + 5x^2 + 5x + 4) = 0
Now, we set each factor equal to zero and solve for x:
x - 5 = 0
x = 5
x^3 + 5x^2 + 5x + 4 = 0
Unfortunately, we cannot factor this further using simple algebraic methods. Therefore, the only solution is x = 5.
x^(3)-3x^(2)-4=(1)/(x-1)+5
what are the 2 x=
1 answer