Change the subject of the formula to the variable indicated?

Question

Solve for b when S=c-b/b-a

show working please

Answer 1

You may have forgotten the parens around b-a, 'cuz
otherwise b cancels out as b/b=1 so I'll assume you mean
S=c-b/(b-a)

S-c= -b/(b-a)
(b-a)(S-c)=-b
Sb-Sa-bc+ac+b=0
b(S-c+1)=Sa-ac
b = a(S-c)/(S-c+1)

But then you might have meant
S=(c-b)/(b-a) Lack of parens makes it ambiguous.
Sb-Sa=c-b
Sb+b=c+Sa
b(S+1)=c+Sa
b=(c+Sa)/(S+1)

Answer 2

Make b the subject of the formula S = c - b/b -a

Multiply both sides by (b - a)

==> S(b - a) = (c - b)

Multiply out the bracket on the LHS

==> Sb - Sa = c - b

Add b and Sa to both sides

==> Sb - Sa + Sa + b = c - b + Sa + b

==> Sb + b = c - Sa

Factorise the LHS

==> b(S + 1) = c - Sa

Divide both sides by (S + 1)

==> b = c - Sa/ S + 1) which was to be achieved

Answer 3

since the denominator cannot be zero then b is unequal to a
S = (c-b)/(b-a) <=> S(b-a) = c-b <=> b(S+1) = c+a
we have these cases:
if (S+1 = 0)and(c+a = 0) then any b which is a subset of R and is unequal to a is a root of the equation
if ((S+1=0)and(c+a <> 0)) or ((S+1<>0)and(a+c = 0)) then the equation has no root
if (s+1<>0)and(c+a<>0) then b = (c+a)/(S+1)

Answer 4

My friend, simply multiply both sides by the denominator (b-a). Expand the brackets to get sb-sa on noe side. Whack sa on the RHS and b to the LHS so the equation now reads:

sb-b = sa+c

Then divide through by (s-1) and youll have the answer

Answer 5

S=(c-b)/(b-a)
=>S*(b-a)=(c-b)
=>S*b-S*a=c-b
=>S*b-b=c-S*a
=>b*(S-1)=c-S*a
=>b=(c-S*a) / (S-1)

Thats the answer