# Solve for x 1/(x^2)-4=10/x

Add to both sides of the equation.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factors for are , which is multiplied by each other times.
occurs times.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Multiply by .
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Solve the equation.
Rewrite the equation as .
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
The final answer is the combination of both solutions.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for x 1/(x^2)-4=10/x

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