Combine and .

Add to both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

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.

Since has no factors besides and .

is a prime number

Since has no factors besides and .

is a prime number

has factors of and .

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

The LCM of is .

Multiply by .

Multiply by .

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 LCM for is the numeric part multiplied by the variable part.

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

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify each term.

Rewrite using the commutative property of multiplication.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Rewrite the equation as .

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

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 .

Subtract from .

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 u -5/(3u)-3=3/2u+7/4