1a+1b=c

Subtract 1b from both sides of the equation.

1a=c-1b

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

a,1,b

Since a,1,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,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 b1 is b itself.

b1=b

b occurs 1 time.

The LCM of a1,b1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

a⋅b

Multiply a by b.

ab

ab

Multiply each term in 1a=c-1b by ab in order to remove all the denominators from the equation.

1a⋅(ab)=c⋅(ab)-1b⋅(ab)

Cancel the common factor of a.

Factor a out of ab.

1a⋅(a(b))=c⋅(ab)-1b⋅(ab)

Cancel the common factor.

1a⋅(ab)=c⋅(ab)-1b⋅(ab)

Rewrite the expression.

b=c⋅(ab)-1b⋅(ab)

b=c⋅(ab)-1b⋅(ab)

Simplify each term.

Cancel the common factor of b.

Move the leading negative in -1b into the numerator.

b=cab+-1b⋅(ab)

Factor b out of ab.

b=cab+-1b⋅(ba)

Cancel the common factor.

b=cab+-1b⋅(ba)

Rewrite the expression.

b=cab-1⋅a

b=cab-1⋅a

Rewrite -1a as -a.

b=cab-a

b=cab-a

b=cab-a

Rewrite the equation as cab-a=b.

cab-a=b

Factor a out of cab-a.

Factor a out of cab.

a(cb)-a=b

Factor a out of -a.

a(cb)+a⋅-1=b

Factor a out of a(cb)+a⋅-1.

a(cb-1)=b

a(cb-1)=b

Divide each term by cb-1 and simplify.

Divide each term in a(cb-1)=b by cb-1.

a(cb-1)cb-1=bcb-1

Cancel the common factor of cb-1.

Cancel the common factor.

a(cb-1)cb-1=bcb-1

Divide a by 1.

a=bcb-1

a=bcb-1

a=bcb-1

a=bcb-1

Solve for a 1/a+1/b=c