8/(2x+3y) +21/(2x-3y)=11; 5/(2x+3y) +7/(2x-3y)=-6;

Given equations are
{tex}\frac{8}{2x - 3y}{/tex} + {tex}\frac{21}{2x + 3y}{/tex} = 11...(i)
{tex}\frac{5}{2x - 3y}{/tex} + {tex}\frac{7}{2x + 3y}{/tex} = 6 ....(ii)
Putting {tex}\frac{1}{2x - 3y}{/tex} = A and {tex}\frac{1}{2x + 3y}{/tex} = B in equation (i) & (ii) so that we may get the pair of linear equations in variables A & B as following :-
8A + 21B = 11 ...(iii).    and 5A + 7B = 6...(iv)
Multiplying eq. (iv) by 3 & then subtracting eq. (iii) from it , we get ;

{tex}\Rightarrow{/tex} A = 1 
Substituting A = 1 in eq. (iii) ,
8 {tex}{/tex}× 1 + 21B = 11
{tex}\Rightarrow{/tex} 21B = 3
{tex}\Rightarrow{/tex} B = {tex}\frac{1}{7}{/tex}
Since, A = 1
{tex}\Rightarrow{/tex} {tex}\frac{1}{2x - 3y}{/tex} = 1
{tex}\Rightarrow{/tex} 2x - 3y  = 1...(vi)
Where B = {tex}\frac{1}{7}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac{1}{2x + 3y}{/tex} = {tex}\frac{1}{7}{/tex}
{tex}\Rightarrow{/tex}2x + 3y = 7...(vii)
Adding (vi) and (vii), we get

{tex}\Rightarrow{/tex}x = 2
Substituting x = 2 in eq.(vi), 
2{tex}{/tex}× 2 - 3y = 1
{tex}\Rightarrow{/tex} -3y = -3
{tex}\Rightarrow{/tex} y = 1
{tex}\therefore{/tex} x  = 2, y = 1.