How do you solve #\frac { b } { b + 7} - 9= \frac { - 7} { b + 7}#?

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Answer 1 · 2017-05-25T02:29:53

No solution

Multiply both sides by #b+7#. Note that this means that #b!=-7#:

#(b+7)(b/(b+7)-9)=(b+7)(-7/(b+7))#

This becomes:

#b-9b-63=-7#

Consolidate the #b#s:

#-8b-63=-7#

Add #63# to both sides:

#-8b-63+63=-7+63#

This becomes:

#-8b=56#

Divide both sides by #-8#:

#(-8b)/-8=56/-8#

This becomes:

#b=-7#

However, don't forget about the initial condition. #b# is not allowed to be #-7#. So we have no solution.