Question 1152135
Simplify {{{ (a(b+c) + (b+c)^2)/(b^2-c^2 + ab-ac) }}}
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<pre>
{{{ (a(b+c) + (b+c)^2)/(b^2-c^2 + ab-ac) =  (b+c)/(b-c) }}} with restriction {{{a+b+c <> 0 }}} and {{{ b-c <> 0 }}}


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The work-out:  

{{{ (a(b+c) + (b+c)^2)/(b^2-c^2 + ab-ac) = ((b+c)(a) + (b+c)(b+c))/ ((b+c)(b-c)+(a)(b-c)) = ((b+c)(a+b+c))/((b-c)(a+b+c))) }}}

then cancel the a+b+c factor from numerator and denominator.