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 four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.

Steps to find the LCM for are:

1. Find the LCM for the numeric part .

2. Find the LCM for the variable part .

3. Find the LCM for the compound variable part .

4. Multiply each LCM together.

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

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.

The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.

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

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Simplify .

Simplify each term.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Move to the left of .

Apply the distributive property.

Multiply by .

Add and .

Since is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Subtract from both sides of the equation.

Subtract from .

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

Factor out of .

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 .

The final answer is the combination of both solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for w 9/w+5=8/(w-8)