Question 1122357
Not clear if you mean it exactly as posted or not.

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Solve for x. 
a^2/b^2= x+b/x+a where b is not equal to 0 and a is not equal to +,- b 
The dash means fraction.
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This might not be what you wanted.


If equation is really  {{{a^2/b^2=(x+b)/(x+a)}}}


{{{a^2x+a^3=b^2x+b^3}}}

{{{a^2x-b^2x=b^3-a^3}}}

{{{(a^2-b^2)x=b^3-a^3}}}

{{{x=(b^3-a^3)/(a^2-b^2)}}},

{{{x=((b-a)(b^2+ab+a^2))/(a^2-b^2)}}}, {{{difference_of_cubes_formula}}}

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

{{{highlight(x=(-(b^2+ab+a^2))/(a+b))}}}