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The equation is not well specified... you should use parentheses for making it clear.

\frac{3}{2x+y}-\frac{4}{2x-y}=5\\\\\frac{5}{2x+y}+\frac{3}{2x-y}=\frac{14}{3}\\\\Let\ \frac{1}{2x+y}=X\ \ ,and\ \ \frac{1}{2x-y}=Y\\\\So,\ 3X-4Y=5\ \ ---(1) \\5X+3Y=\frac{14}{3}\ \ --(2)\\\\Do\ (1)*3+(2)*4\ to\ get:\\\\29X=101/3\ \ X=\frac{101}{87}\\\\Y=\frac{3X-5}{4}=-\frac{11}{29}\\\\So,\ 2x+y=1/X=\frac{87}{101},\ \ ---(3)\\\\2x-y=1/Y=-\frac{29}{11},\ \ (4)\\\\Add\ (4)\ and\ (3)\ to\ get:\\\\x=-\frac{17*29}{11*101}\\\\y=2x+\frac{29}{11}=\frac{67*29}{11*101}

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select best answer pls
yes its right but i have a question
we can't simplify x and y further?
can we simplify x and y further???????????