Solve the Rational Equation for x 1/(x-1)-1=x/(x-1)

Solve the Rational Equation for x 1/(x-1)-1=x/(x-1)
Add to 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.
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 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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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify the right 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.
Multiply by .
Add and .
Solve the equation.
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Rewrite the equation as .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Add and .
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Exclude the solutions that do not make true.
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Name

Name four hundred thirty-five million six hundred eighty-seven thousand three hundred six

Interesting facts

  • 435687306 has 32 divisors, whose sum is 878169600
  • The reverse of 435687306 is 603786534
  • Previous prime number is 439

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 42
  • Digital Root 6

Name

Name one billion six hundred twenty-nine million five hundred fifteen thousand eight hundred thirty-seven

Interesting facts

  • 1629515837 has 4 divisors, whose sum is 1682080896
  • The reverse of 1629515837 is 7385159261
  • Previous prime number is 31

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion six hundred ninety-eight million nine hundred thirty-five thousand two hundred fifty-two

Interesting facts

  • 1698935252 has 16 divisors, whose sum is 3833752032
  • The reverse of 1698935252 is 2525398961
  • Previous prime number is 343

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5