# Solve by Factoring (2x)/(x-2)=5+(4x^2)/(x-2)

Move all the expressions to the left side of the equation.
Move to the left side of the equation by subtracting it from both sides.
Move to the left side of the equation by subtracting it from both sides.
Simplify .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Combine the numerators over the common denominator.
Factor by grouping.
Reorder terms.
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, .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Combine the numerators over the common denominator.
Factor by grouping.
Reorder terms.
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, .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Find the LCD of the terms in the equation.
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 LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Simplify terms.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply.
Multiply by .
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 by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Solve the equation.
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor.
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, .
Remove unnecessary parentheses.
Multiply each term in by
Multiply each term in by .
Simplify .
Simplify by multiplying through.
Apply the distributive property.
Multiply.
Multiply by .
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 by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
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.
Solve by Factoring (2x)/(x-2)=5+(4x^2)/(x-2)