Solve for m 1/(2m^2)=1/m-1/2

Solve for m 1/(2m^2)=1/m-1/2
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
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Since has no factors besides and .
is a prime number
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 .
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.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify each term.
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Rewrite using the commutative property of multiplication.
Combine and .
Cancel the common factor of .
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Factor out of .
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.
Rewrite as .
Solve the equation.
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Rewrite the equation as .
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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Let . Substitute for all occurrences of .
Factor by grouping.
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Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Multiply by .
Multiply by .
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Replace the left side with the factored expression.
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 .
Subtract from both sides of the equation.
Multiply each term in by
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Multiply each term in by .
Multiply .
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Multiply by .
Multiply by .
Multiply by .
The final solution is all the values that make true.
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Name

Name one billion eight hundred seventy-eight million one hundred fifty-three thousand three hundred forty-two

Interesting facts

  • 1878153342 has 16 divisors, whose sum is 2890905600
  • The reverse of 1878153342 is 2433518781
  • Previous prime number is 2551

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name eight hundred ninety-nine million four hundred forty-five thousand five hundred fifty-seven

Interesting facts

  • 899445557 has 4 divisors, whose sum is 899536716
  • The reverse of 899445557 is 755544998
  • Previous prime number is 11257

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 56
  • Digital Root 2

Name

Name one billion three hundred seventeen million six hundred ninety-eight thousand forty-four

Interesting facts

  • 1317698044 has 32 divisors, whose sum is 3228770160
  • The reverse of 1317698044 is 4408967131
  • Previous prime number is 89

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7