x-22x+1=x+1x

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

2x,1,x

Since 2x,1,x contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 2,1,1 then find LCM for the variable part x1,x1.

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 2 has no factors besides 1 and 2.

2 is a prime number

The number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 2,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2

The factor for x1 is x itself.

x1=x

x occurs 1 time.

The LCM of x1,x1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

x

The LCM for 2x,1,x is the numeric part 2 multiplied by the variable part.

2x

2x

Multiply each term in x-22x+1=x+1x by 2x in order to remove all the denominators from the equation.

x-22x⋅(2x)+1⋅(2x)=x+1x⋅(2x)

Simplify x-22x⋅(2x)+1⋅(2x).

Simplify each term.

Rewrite using the commutative property of multiplication.

2x-22xx+1⋅(2x)=x+1x⋅(2x)

Cancel the common factor of 2.

Factor 2 out of 2x.

2x-22(x)x+1⋅(2x)=x+1x⋅(2x)

Cancel the common factor.

2x-22xx+1⋅(2x)=x+1x⋅(2x)

Rewrite the expression.

x-2xx+1⋅(2x)=x+1x⋅(2x)

x-2xx+1⋅(2x)=x+1x⋅(2x)

Cancel the common factor of x.

Cancel the common factor.

x-2xx+1⋅(2x)=x+1x⋅(2x)

Rewrite the expression.

x-2+1⋅(2x)=x+1x⋅(2x)

x-2+1⋅(2x)=x+1x⋅(2x)

Multiply 2x by 1.

x-2+2x=x+1x⋅(2x)

x-2+2x=x+1x⋅(2x)

Add x and 2x.

3x-2=x+1x⋅(2x)

3x-2=x+1x⋅(2x)

Simplify x+1x⋅(2x).

Rewrite using the commutative property of multiplication.

3x-2=2x+1xx

Combine 2 and x+1x.

3x-2=2(x+1)xx

Cancel the common factor of x.

Cancel the common factor.

3x-2=2(x+1)xx

Rewrite the expression.

3x-2=2(x+1)

3x-2=2(x+1)

Apply the distributive property.

3x-2=2x+2⋅1

Multiply 2 by 1.

3x-2=2x+2

3x-2=2x+2

3x-2=2x+2

Move all terms containing x to the left side of the equation.

Subtract 2x from both sides of the equation.

3x-2-2x=2

Subtract 2x from 3x.

x-2=2

x-2=2

Move all terms not containing x to the right side of the equation.

Add 2 to both sides of the equation.

x=2+2

Add 2 and 2.

x=4

x=4

x=4

Solve for x (x-2)/(2x)+1=(x+1)/x