# Solve for a 2/a+4/b=1/c

2a+4b=1c
Subtract 4b from both sides of the equation.
2a=1c-4b
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.
a,c,b
Since a,c,b contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1 then find LCM for the variable part a1,c1,b1.
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 a1 is a itself.
a1=a
a occurs 1 time.
The factor for c1 is c itself.
c1=c
c occurs 1 time.
The factor for b1 is b itself.
b1=b
b occurs 1 time.
The LCM of a1,c1,b1 is the result of multiplying all prime factors the greatest number of times they occur in either term.
a⋅c⋅b
Multiply ac by b.
acb
acb
Multiply each term by acb and simplify.
Multiply each term in 2a=1c-4b by acb in order to remove all the denominators from the equation.
2a⋅(acb)=1c⋅(acb)-4b⋅(acb)
Cancel the common factor of a.
Factor a out of acb.
2a⋅(a(cb))=1c⋅(acb)-4b⋅(acb)
Cancel the common factor.
2a⋅(a(cb))=1c⋅(acb)-4b⋅(acb)
Rewrite the expression.
2⋅(cb)=1c⋅(acb)-4b⋅(acb)
2cb=1c⋅(acb)-4b⋅(acb)
Simplify each term.
Cancel the common factor of c.
Factor c out of acb.
2cb=1c⋅(c(ab))-4b⋅(acb)
Cancel the common factor.
2cb=1c⋅(c(ab))-4b⋅(acb)
Rewrite the expression.
2cb=ab-4b⋅(acb)
2cb=ab-4b⋅(acb)
Cancel the common factor of b.
Move the leading negative in -4b into the numerator.
2cb=ab+-4b⋅(acb)
Factor b out of acb.
2cb=ab+-4b⋅(b(ac))
Cancel the common factor.
2cb=ab+-4b⋅(b(ac))
Rewrite the expression.
2cb=ab-4⋅(ac)
2cb=ab-4ac
2cb=ab-4ac
2cb=ab-4ac
Solve the equation.
Rewrite the equation as ab-4ac=2cb.
ab-4ac=2cb
Factor a out of ab-4ac.
Factor a out of ab.
a(b)-4ac=2cb
Factor a out of -4ac.
a(b)+a(-4c)=2cb
Factor a out of a(b)+a(-4c).
a(b-4c)=2cb
a(b-4c)=2cb
Divide each term by b-4c and simplify.
Divide each term in a(b-4c)=2cb by b-4c.
a(b-4c)b-4c=2cbb-4c
Cancel the common factor of b-4c.
Cancel the common factor.
a(b-4c)b-4c=2cbb-4c
Divide a by 1.
a=2cbb-4c
a=2cbb-4c
a=2cbb-4c
a=2cbb-4c
Solve for a 2/a+4/b=1/c

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