Solve for y 1/2y-2/7=1/(7y)-7/2

Math
Combine and .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Add and .
Move the negative in front of the fraction.
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.
Since has no factors besides and .
is a prime number
Since has no factors besides and .
is a prime number
has factors of and .
Multiply by .
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.
The LCM for is the numeric part multiplied by the variable part.
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 .
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Rewrite using the commutative property of multiplication.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by by adding the exponents.
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Move .
Multiply by .
Simplify each term.
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Rewrite using the commutative property of multiplication.
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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.
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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Raise to the power of .
Multiply by .
Multiply by .
Add and .
Multiply by .
The final answer is the combination of both solutions.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for y 1/2y-2/7=1/(7y)-7/2

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