# Solve by Factoring x/(x-3)+x/2=(6x)/(2x-6)

Move to the left side of the equation by subtracting it from both sides.
Simplify .
Simplify terms.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine fractions with similar denominators.
Subtract from .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Subtract from .
Simplify terms.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine fractions with similar denominators.
Subtract from .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Subtract from .
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.
Since has no factors besides and .
is a prime 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.
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Rewrite using the commutative property of multiplication.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Simplify the expression.
Multiply by .
Move to the left of .
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Solve the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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 .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
Solve by Factoring x/(x-3)+x/2=(6x)/(2x-6)