k+1k=2

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

1,k,1

Since 1,k,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1 then find LCM for the variable part k1.

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

Not prime

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

1

The factor for k1 is k itself.

k1=k

k occurs 1 time.

The LCM of k1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

k

k

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

k⋅k+1k⋅k=2⋅k

Simplify each term.

Multiply k by k.

k2+1k⋅k=2⋅k

Cancel the common factor of k.

Cancel the common factor.

k2+1k⋅k=2⋅k

Rewrite the expression.

k2+1=2⋅k

k2+1=2⋅k

k2+1=2k

k2+1=2k

Subtract 2k from both sides of the equation.

k2+1-2k=0

Factor using the perfect square rule.

Rearrange terms.

k2-2k+1=0

Rewrite 1 as 12.

k2-2k+12=0

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅k⋅-1

Simplify.

2ab=-2k

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=k and b=-1.

(k-1)2=0

(k-1)2=0

Set the k-1 equal to 0.

k-1=0

Add 1 to both sides of the equation.

k=1

k=1

Solve for k k+1/k=2