Subtract from both sides of the equation.

Subtract from 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.

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.

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 factor for is itself.

occurs time.

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 .

Multiply each term in by in order to remove all the denominators from the equation.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify each term.

Multiply by by adding the exponents.

Move .

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Rewrite the equation as .

Move to the left side of the equation by subtracting it from both sides.

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify the numerator.

Apply the distributive property.

Multiply .

Multiply by .

Multiply by .

Multiply .

Multiply by .

Multiply by .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply by .

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Add and .

Reorder and .

Add and .

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Move to the left of .

Rewrite as .

Multiply by .

The final answer is the combination of both solutions.

Solve for t 1/f+1/t+1/k=t