# Solve for m 3/(16m^2-81)=-5/(4m^2+9m)

316m2-81=-54m2+9m
Factor each term.
Rewrite 16m2 as (4m)2.
3(4m)2-81=-54m2+9m
Rewrite 81 as 92.
3(4m)2-92=-54m2+9m
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=4m and b=9.
3(4m+9)(4m-9)=-54m2+9m
Factor m out of 4m2+9m.
Factor m out of 4m2.
3(4m+9)(4m-9)=-5m(4m)+9m
Factor m out of 9m.
3(4m+9)(4m-9)=-5m(4m)+m⋅9
Factor m out of m(4m)+m⋅9.
3(4m+9)(4m-9)=-5m(4m+9)
3(4m+9)(4m-9)=-5m(4m+9)
3(4m+9)(4m-9)=-5m(4m+9)
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.
(4m+9)(4m-9),m(4m+9)
Since (4m+9)(4m-9),m(4m+9) contain both numbers and variables, there are four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.
Steps to find the LCM for (4m+9)(4m-9),m(4m+9) are:
1. Find the LCM for the numeric part 1,1.
2. Find the LCM for the variable part m1.
3. Find the LCM for the compound variable part 4m+9,4m-9,4m+9.
4. Multiply each LCM together.
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
The LCM of 1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The factor for m1 is m itself.
m1=m
m occurs 1 time.
The LCM of m1 is the result of multiplying all prime factors the greatest number of times they occur in either term.
m
The factor for 4m+9 is 4m+9 itself.
(4m+9)=4m+9
(4m+9) occurs 1 time.
The factor for 4m-9 is 4m-9 itself.
(4m-9)=4m-9
(4m-9) occurs 1 time.
The factor for 4m+9 is 4m+9 itself.
(4m+9)=4m+9
(4m+9) occurs 1 time.
The LCM of 4m+9,4m-9,4m+9 is the result of multiplying all factors the greatest number of times they occur in either term.
(4m+9)(4m-9)
The Least Common Multiple LCM of some numbers is the smallest number that the numbers are factors of.
m(4m+9)(4m-9)
m(4m+9)(4m-9)
Multiply each term by m(4m+9)(4m-9) and simplify.
Multiply each term in 3(4m+9)(4m-9)=-5m(4m+9) by m(4m+9)(4m-9) in order to remove all the denominators from the equation.
3(4m+9)(4m-9)⋅(m(4m+9)(4m-9))=-5m(4m+9)⋅(m(4m+9)(4m-9))
Cancel the common factor of (4m+9)(4m-9).
Factor (4m+9)(4m-9) out of m(4m+9)(4m-9).
3(4m+9)(4m-9)⋅((4m+9)(4m-9)(m))=-5m(4m+9)⋅(m(4m+9)(4m-9))
Cancel the common factor.
3(4m+9)(4m-9)⋅((4m+9)(4m-9)m)=-5m(4m+9)⋅(m(4m+9)(4m-9))
Rewrite the expression.
3⋅m=-5m(4m+9)⋅(m(4m+9)(4m-9))
3m=-5m(4m+9)⋅(m(4m+9)(4m-9))
Simplify -5m(4m+9)⋅(m(4m+9)(4m-9)).
Cancel the common factor of m(4m+9).
Move the leading negative in -5m(4m+9) into the numerator.
3m=-5m(4m+9)⋅(m(4m+9)(4m-9))
Cancel the common factor.
3m=-5m(4m+9)⋅(m(4m+9)(4m-9))
Rewrite the expression.
3m=-5⋅(4m-9)
3m=-5⋅(4m-9)
Apply the distributive property.
3m=-5(4m)-5⋅-9
Multiply.
Multiply 4 by -5.
3m=-20m-5⋅-9
Multiply -5 by -9.
3m=-20m+45
3m=-20m+45
3m=-20m+45
3m=-20m+45
Solve the equation.
Move all terms containing m to the left side of the equation.
Add 20m to both sides of the equation.
3m+20m=45
23m=45
23m=45
Divide each term by 23 and simplify.
Divide each term in 23m=45 by 23.
23m23=4523
Cancel the common factor of 23.
Cancel the common factor.
23m23=4523
Divide m by 1.
m=4523
m=4523
m=4523
m=4523
The result can be shown in multiple forms.
Exact Form:
m=4523
Decimal Form:
m=1.95652173…
Mixed Number Form:
m=12223
Solve for m 3/(16m^2-81)=-5/(4m^2+9m)

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