(3m2)=m-43m2+23m2

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 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

Add -4 and 2.

9=m-2

9=m-2

9=m-2

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

Add 9 and 2.

m=11

m=11

m=11

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