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factor (1)/(x^(2))-(1)/(x)=6
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Introduce new variable y = . (1)
Then your equation will take the form
= 6, or, equivalently,
= 0. (2)
The left side quadratic polynomial can be easily factored
(y-3)*(y+2) = 0. (3)
It gives the roots of the equation y = 3 and y = -2.
Let us consider both cases.
1. If y = 3, then x = = , due to (1).
2. If y = -2, then x = = .
Answer. The original equation has the roots and .
Solved.
Notice. The formulation of the problem in your post is not exactly adequate.
The ideally balanced formulation is THIS:
Solve the equation (1)/(x^(2))-(1)/(x)=6 using factoring.