Question 279580
your equation is:


{{{(q+4)/(q-1) + (q)/(q+1) = 2}}}


multiply both sides of this equation by {{{(q-1)*(q+1)}}} to get:


{{{(q+4)*(q-1)*(q+1)/(q-1) + (q)*(q-1)*(q+1)/(q+1) = 2*(q-1)*(q+1)}}} which becomes:


{{{(q+4)*(q+1) + (q)*(q-1) = 2*(q-1)*(q+1)}}}


simplify by removing parentheses to get:


{{{q^2 + 5q + 4 + q^2 - q = 2q^2 - 2}}}


combine like terms to get:


{{{2q^2 + 4q + 4 = 2q^2 - 2}}}


subtract {{{2q^2}}} from both sides of the equation and subtract 4 from both sides of the equation and combine like terms to get:


4q = -6


divide both sides of the equation by 4 to get:


q = -6/4 = -3/2


plug that value of q into your original equation to confirm that the equation is true.


I did that and confirmed the original equation is true.


your answer is that q = -3/2