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# Solve for m (2m)/(m-1)+(m-5)/(m^2-1)=1

Factor each term.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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.
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 factor for is itself.
occurs time.
The factor for is itself.
occurs time.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term in by to eliminate the fractions.
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Multiply each term in by .
Simplify the left side.
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Simplify each term.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by by adding the exponents.
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Move .
Multiply by .
Multiply by .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
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Multiply by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify terms.
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Combine the opposite terms in .
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Reorder the factors in the terms and .
Subtract from .
Simplify each term.
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Multiply by .
Multiply by .
Solve the equation.
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Move all terms containing to the left side of the equation.
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Subtract from both sides of the equation.
Subtract from .
Add to both sides of the equation.
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Add to both sides of the equation.
Set equal to and solve for .
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Set equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Exclude the solutions that do not make true.