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 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 in order to remove all the denominators from the equation.

Simplify .

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Multiply by .

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.

Apply the distributive property.

Multiply by .

Multiply by .

Multiply by .

Simplify by adding terms.

Combine the opposite terms in .

Subtract from .

Add and .

Subtract from .

Simplify .

Multiply by .

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 .

Multiply by .

Multiply by .

Add and .

Add and .

Subtract from both sides of the equation.

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

Factor out of .

Reorder and .

Factor out of .

Factor out of .

Rewrite as .

Factor out of .

Factor out of .

Multiply each term in by

Multiply each term in by .

Simplify .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Use the quadratic formula to find the solutions.

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

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Add and .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Simplify .

The final answer is the combination of both solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for m (2m)/(2m+3)-(2m)/(2m-3)=1