7. Solve
for *x* and check.

First, clear denominators. Multiply both sides by *x* + *b*.

Remove parentheses

Transpose all terms that involve *x* to one side and the terms that
do not to the other side.

Factor out the *x*

Divide by the coefficient of the unknown

*c* cannot be equal to one or else you will have a zero denominator
in the solution. If *c* = 1, then the top of the fraction and the
bottom have to be the same. That will happen only if *a* = b, in which
case any value of *x* will be a solution. Otherwise, there will be no
value of *x* which will work

**Check**. Copy down the original equation except where you see
an *x*, copy down the solution in parentheses.

On the left we have a compound fraction. Add the fractions on both
the top and bottom in order to prepare for inverting and multiplying.
The common denominator is 1 - *c*.

After we add the fractions

we find some like terms that cancel.

We are now ready to invert and multiply. Let us factor out the c from the t wo terns in the top of the top.

After we cancel we get

Note that in the check, in addition to the requirement that *c* is
not equal to 1, there is another occasion to get zero denominators in
the check. If *a* = *b* there will be a zero denominator in the check. If
*a* = *b*, then the fraction will always reduce to 1, and so any value of
*x* would work if c were 1, but no value would work if &mbsp; *c* were not 1. In
either case, there is not a unique solution, and this is manifested
by the problems with zero denominators.