# Solve by Factoring 3/(x^2-3x)+4/x=1/(x-3)

Move to the left side of the equation by subtracting it from both sides.
Simplify .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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 .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Cancel the common factor of and .
Rewrite as .
Factor out of .
Factor out of .
Reorder terms.
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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 .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Cancel the common factor of and .
Rewrite as .
Factor out of .
Factor out of .
Reorder terms.
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
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.
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
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.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Since , there are no solutions.
No solution
Solve by Factoring 3/(x^2-3x)+4/x=1/(x-3)