Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

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 <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of <math><mstyle displaystyle="true"><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mstyle></math> is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> itself.

The LCM of <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> is the result of multiplying all factors the greatest number of times they occur in either term.

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Rewrite the equation as <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>1</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Exclude the solutions that do not make <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mstyle></math> true.

Do you know how to Solve the Rational Equation for x 1/(x-1)-1=x/(x-1)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

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

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

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

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

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

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

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

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

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