# Solve for v 3/(v+7)+6/v=-7/(v^2+7v)

3v+7+6v=-7v2+7v
Factor each term.
Factor v out of v2+7v.
Factor v out of v2.
3v+7+6v=-7v⋅v+7v
Factor v out of 7v.
3v+7+6v=-7v⋅v+v⋅7
Factor v out of v⋅v+v⋅7.
3v+7+6v=-7v(v+7)
3v+7+6v=-7v(v+7)
Move the negative in front of the fraction.
3v+7+6v=-7v(v+7)
3v+7+6v=-7v(v+7)
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.
v+7,v,v(v+7)
Since v+7,v,v(v+7) 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 v+7,v,v(v+7) are:
1. Find the LCM for the numeric part 1,1,1.
2. Find the LCM for the variable part v1,v1.
3. Find the LCM for the compound variable part v+7,v+7.
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 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The factor for v1 is v itself.
v1=v
v occurs 1 time.
The LCM of v1,v1 is the result of multiplying all prime factors the greatest number of times they occur in either term.
v
The factor for v+7 is v+7 itself.
(v+7)=v+7
(v+7) occurs 1 time.
The LCM of v+7,v+7 is the result of multiplying all factors the greatest number of times they occur in either term.
v+7
The Least Common Multiple LCM of some numbers is the smallest number that the numbers are factors of.
v(v+7)
v(v+7)
Multiply each term by v(v+7) and simplify.
Multiply each term in 3v+7+6v=-7v(v+7) by v(v+7) in order to remove all the denominators from the equation.
3v+7⋅(v(v+7))+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
Simplify 3v+7⋅(v(v+7))+6v⋅(v(v+7)).
Simplify each term.
Cancel the common factor of v+7.
Factor v+7 out of v(v+7).
3v+7⋅((v+7)v)+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
Cancel the common factor.
3v+7⋅((v+7)v)+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
Rewrite the expression.
3⋅v+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
3⋅v+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
Cancel the common factor of v.
Cancel the common factor.
3v+6v⋅(v(v+7))=-7v(v+7)⋅(v(v+7))
Rewrite the expression.
3v+6⋅(v+7)=-7v(v+7)⋅(v(v+7))
3v+6⋅(v+7)=-7v(v+7)⋅(v(v+7))
Apply the distributive property.
3v+6v+6⋅7=-7v(v+7)⋅(v(v+7))
Multiply 6 by 7.
3v+6v+42=-7v(v+7)⋅(v(v+7))
3v+6v+42=-7v(v+7)⋅(v(v+7))
9v+42=-7v(v+7)⋅(v(v+7))
9v+42=-7v(v+7)⋅(v(v+7))
Cancel the common factor of v(v+7).
Move the leading negative in -7v(v+7) into the numerator.
9v+42=-7v(v+7)⋅(v(v+7))
Cancel the common factor.
9v+42=-7v(v+7)⋅(v(v+7))
Rewrite the expression.
9v+42=-7
9v+42=-7
9v+42=-7
Solve the equation.
Move all terms not containing v to the right side of the equation.
Subtract 42 from both sides of the equation.
9v=-7-42
Subtract 42 from -7.
9v=-49
9v=-49
Divide each term by 9 and simplify.
Divide each term in 9v=-49 by 9.
9v9=-499
Cancel the common factor of 9.
Cancel the common factor.
9v9=-499
Divide v by 1.
v=-499
v=-499
Move the negative in front of the fraction.
v=-499
v=-499
v=-499
The result can be shown in multiple forms.
Exact Form:
v=-499
Decimal Form:
v=-5.4‾
Mixed Number Form:
v=-549
Solve for v 3/(v+7)+6/v=-7/(v^2+7v)

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