Solve for z z=1/(z^2)

Math
Subtract from both sides of the equation.
Find the LCD of the terms in the equation.
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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 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.
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Multiply each term in by in order to remove all the denominators from the equation.
Simplify each term.
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Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Cancel the common factor of .
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Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Multiply by .
Solve the equation.
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Add to both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
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Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Multiply by .
One to any power is one.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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One to any power is one.
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by .
The final answer is the combination of both solutions.
The final solution is all the values that make true.
Solve for z z=1/(z^2)

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