Question 107637
Your problem as written doesn't make sense, but I'm going to make an assumption that does and go with that.  What I think you meant was:


{{{y1=1/(x+7)}}}, {{{y2=2/(x+3)}}}, {{{y3=(-4)/(x^2+10x+21)}}}, and {{{y1+y2=y3}}}


That means we can say:


{{{(1/(x+7))+(2/(x+3))=(-4)/(x^2+10x+21)}}}


To add the two terms on the left side, we need a Lowest Common Denominator, given by:


{{{(x+7)(x+3)=x^2+10x+21}}}


Now we have:


{{{((x+3)/(x^2+10x+21))+(2(x+7)/(x^2+10x+21))=(-4)/(x^2+10x+21)}}}


Simplify:


{{{(3x+17)/(x^2+10x+21)=(-4)/(x^2+10x+21)}}}


Since the denominators are equal on both sides, the numerators must be equal as well for the statement to be true, therefore:


{{{3x+17=-4}}}
{{{3x=-21}}}
{{{x=-21/3=-7}}}


But that causes a problem because -7 is not in the domain of either the y1 or y3 functions.  x=-7 leads to a zero denominator in each case.  Therefore, there are no values of x that satisfy the given conditions.  Presuming my assumptions about the construct of the original problem were correct, that is.