# Solve for m 3/(2m+4)=1/(m+2)-2

32m+4=1m+2-2
Factor 2 out of 2m+4.
Factor 2 out of 2m.
32(m)+4=1m+2-2
Factor 2 out of 4.
32m+2⋅2=1m+2-2
Factor 2 out of 2m+2⋅2.
32(m+2)=1m+2-2
32(m+2)=1m+2-2
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.
2(m+2),m+2,1
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 2 has no factors besides 1 and 2.
2 is a prime number
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 2,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2
The factor for m+2 is m+2 itself.
(m+2)=m+2
(m+2) occurs 1 time.
The LCM of m+2,m+2 is the result of multiplying all factors the greatest number of times they occur in either term.
m+2
The Least Common Multiple LCM of some numbers is the smallest number that the numbers are factors of.
2(m+2)
2(m+2)
Multiply each term by 2(m+2) and simplify.
Multiply each term in 32(m+2)=1m+2-2 by 2(m+2) in order to remove all the denominators from the equation.
32(m+2)⋅(2(m+2))=1m+2⋅(2(m+2))-2⋅(2(m+2))
Simplify 32(m+2)⋅(2(m+2)).
Rewrite using the commutative property of multiplication.
232(m+2)(m+2)=1m+2⋅(2(m+2))-2⋅(2(m+2))
Cancel the common factor of 2.
Cancel the common factor.
232(m+2)(m+2)=1m+2⋅(2(m+2))-2⋅(2(m+2))
Rewrite the expression.
3m+2(m+2)=1m+2⋅(2(m+2))-2⋅(2(m+2))
3m+2(m+2)=1m+2⋅(2(m+2))-2⋅(2(m+2))
Cancel the common factor of m+2.
Cancel the common factor.
3m+2(m+2)=1m+2⋅(2(m+2))-2⋅(2(m+2))
Rewrite the expression.
3=1m+2⋅(2(m+2))-2⋅(2(m+2))
3=1m+2⋅(2(m+2))-2⋅(2(m+2))
3=1m+2⋅(2(m+2))-2⋅(2(m+2))
Simplify 1m+2⋅(2(m+2))-2⋅(2(m+2)).
Simplify each term.
Rewrite using the commutative property of multiplication.
3=21m+2(m+2)-2⋅(2(m+2))
Combine 2 and 1m+2.
3=2m+2(m+2)-2⋅(2(m+2))
Cancel the common factor of m+2.
Cancel the common factor.
3=2m+2(m+2)-2⋅(2(m+2))
Rewrite the expression.
3=2-2⋅(2(m+2))
3=2-2⋅(2(m+2))
Apply the distributive property.
3=2-2⋅(2m+2⋅2)
Multiply 2 by 2.
3=2-2⋅(2m+4)
Apply the distributive property.
3=2-2(2m)-2⋅4
Multiply 2 by -2.
3=2-4m-2⋅4
Multiply -2 by 4.
3=2-4m-8
3=2-4m-8
Subtract 8 from 2.
3=-4m-6
3=-4m-6
3=-4m-6
Solve the equation.
Rewrite the equation as -4m-6=3.
-4m-6=3
Move all terms not containing m to the right side of the equation.
Add 6 to both sides of the equation.
-4m=3+6
-4m=9
-4m=9
Divide each term by -4 and simplify.
Divide each term in -4m=9 by -4.
-4m-4=9-4
Cancel the common factor of -4.
Cancel the common factor.
-4m-4=9-4
Divide m by 1.
m=9-4
m=9-4
Move the negative in front of the fraction.
m=-94
m=-94
m=-94
The result can be shown in multiple forms.
Exact Form:
m=-94
Decimal Form:
m=-2.25
Mixed Number Form:
m=-214
Solve for m 3/(2m+4)=1/(m+2)-2

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