Question

Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help

Answer 1

Answer:

see below

Step-by-step explanation:

1/a = 1/b+1/c

Multiply each side of the equation by a

a( 1/a) =a( 1/b+1/c)

1 = a/b + a/c

Then multiply each side of the equation by b

b*1 =b( a/b + a/c)

b = a + ab/c

Then multiply each side of the equation by c

cb = c( a+ ab/c)

bc = ac + ab

We have gotten rid of the fractions

Now we can solve for a

Factor out a on the right side

bc = a( c+b)

Then divide by c+b on each side

bc / ( c+b) = a ( c+b) / ( c+b)

bc / ( c+b) = a

Now we can solve for b

bc = ac + ab

Subtract  ab from each side

bc -ab = ac + ab-ab

bc -ab = ac

Factor out b on the left side side

b( c-a) = ac

Then divide by c-a on each side

b( c-a) / ( c-a) = ac / ( c-a)

b  = ac/ ( c-a)

We can factor out -1

b = -ac/( a-c)

Answer 2

Step-by-step explanation:

1/a = 1/b + 1/c

Multiply both sides by a.

1 = a/b + a/c

Multiply both sides by b.

b = a + ab/c

Multiply both sides by c.

bc = ac + ab

Subtract ab from both sides.

bc − ab = ac

Factor b.

b (c − a) = ac

Divide both sides by c − a.

b = ac / (c − a)