# Solve for m (3/(m^2))=(m-4)/(3m^2)+2/(3m^2)

(3m2)=m-43m2+23m2
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.
m2,3m2,3m2
Since m2,3m2,3m2 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,3,3 then find LCM for the variable part m2,m2,m2.
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 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
Since 3 has no factors besides 1 and 3.
3 is a prime number
The LCM of 1,3,3 is the result of multiplying all prime factors the greatest number of times they occur in either number.
3
The factors for m2 are m⋅m, which is m multiplied by each other 2 times.
m2=m⋅m
m occurs 2 times.
The LCM of m2,m2,m2 is the result of multiplying all prime factors the greatest number of times they occur in either term.
m⋅m
Multiply m by m.
m2
The LCM for m2,3m2,3m2 is the numeric part 3 multiplied by the variable part.
3m2
3m2
Multiply each term by 3m2 and simplify.
Multiply each term in 3m2=m-43m2+23m2 by 3m2 in order to remove all the denominators from the equation.
3m2⋅(3m2)=m-43m2⋅(3m2)+23m2⋅(3m2)
Simplify 3m2⋅(3m2).
Rewrite using the commutative property of multiplication.
33m2m2=m-43m2⋅(3m2)+23m2⋅(3m2)
Multiply 33m2.
Combine 3 and 3m2.
3⋅3m2m2=m-43m2⋅(3m2)+23m2⋅(3m2)
Multiply 3 by 3.
9m2m2=m-43m2⋅(3m2)+23m2⋅(3m2)
9m2m2=m-43m2⋅(3m2)+23m2⋅(3m2)
Cancel the common factor of m2.
Cancel the common factor.
9m2m2=m-43m2⋅(3m2)+23m2⋅(3m2)
Rewrite the expression.
9=m-43m2⋅(3m2)+23m2⋅(3m2)
9=m-43m2⋅(3m2)+23m2⋅(3m2)
9=m-43m2⋅(3m2)+23m2⋅(3m2)
Simplify m-43m2⋅(3m2)+23m2⋅(3m2).
Simplify each term.
Rewrite using the commutative property of multiplication.
9=3m-43m2m2+23m2⋅(3m2)
Cancel the common factor of 3.
Factor 3 out of 3m2.
9=3m-43(m2)m2+23m2⋅(3m2)
Cancel the common factor.
9=3m-43m2m2+23m2⋅(3m2)
Rewrite the expression.
9=m-4m2m2+23m2⋅(3m2)
9=m-4m2m2+23m2⋅(3m2)
Cancel the common factor of m2.
Cancel the common factor.
9=m-4m2m2+23m2⋅(3m2)
Rewrite the expression.
9=m-4+23m2⋅(3m2)
9=m-4+23m2⋅(3m2)
Rewrite using the commutative property of multiplication.
9=m-4+323m2m2
Cancel the common factor of 3.
Factor 3 out of 3m2.
9=m-4+323(m2)m2
Cancel the common factor.
9=m-4+323m2m2
Rewrite the expression.
9=m-4+2m2m2
9=m-4+2m2m2
Cancel the common factor of m2.
Cancel the common factor.
9=m-4+2m2m2
Rewrite the expression.
9=m-4+2
9=m-4+2
9=m-4+2
9=m-2
9=m-2
9=m-2
Solve the equation.
Rewrite the equation as m-2=9.
m-2=9
Move all terms not containing m to the right side of the equation.
Add 2 to both sides of the equation.
m=9+2