# Solve for x 2x+5/2=3/x

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

Since has no factors besides and .

is a prime number

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 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 .

Multiply by .

Multiply by .

Simplify each term.

Rewrite using the commutative property of multiplication.

Multiply .

Combine and .

Multiply by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Add to both sides of the equation.

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

Factor by grouping.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Set the next factor equal to and solve.

Set the next factor equal to .

Subtract from both sides of the equation.

The final solution is all the values that make true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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