how to find restrictions for a literal equation?
example:
(a+x)/(b-x) =c , x=/=b

note: when writing the restrictions, x cannot be part of the restriction because it is the variable we are solving for...(so we do substitution to avoid that??) can someone show the substitution part?

Question

how to find restrictions for a literal equation?
example:
(a+x)/(b-x) =c , x=/=b

note: when writing the restrictions, x cannot be part of the restriction because it is the variable we are solving for...(so we do substitution to avoid that??) can someone show the substitution part?

anonymous · Answer

solve for x

freckles · Answer

So we are solving for x.
You can multiply both sides by (b-x) as a first step
Bur out goal is to eventually gather x terms on one side and non-x terms on the opposite side

freckles · Answer

$$a+x=c(b-x)$$
distribute the c

freckles · Answer

then again gather the x terms on one side and the non-x terms on the other

anonymous · Answer

how would you find restrictions?

anonymous · Answer

i know that the answer is x= (cb-a)/c+1 and the restriction is c=-1 and x cannot equal b

but the problem is that x=/=b cannot be part of the solution because we are using the variable that we are solving for. therefore, we have to substitute the solution in the x=/=b.

so we solve (cb-a)/(c+1) =/= b

after this im stuck.  do we simplify? or can we leave the restriction just like that?