Question

\frac{x+1}{x^2-4}+\frac{5}{2x+4}=\ ???

Answer 1

 

 

Answer 2

x+1              5

------   +   ---------   =    

x²-4           2x+4

 

     Z: 

     x²-4 ≠ 0

     (x+2)(x-2) ≠ 0

     x ≠ -2, x ≠ 2

 

     2x+4 ≠ 0

     2(x+2) ≠ 0

     x ≠ -2

     D = R \ {-2; 2}

 

= (x+1)/[(x+2)(x-2)] + 5/2(x+2) = [2(x+1)+5(x-2)]/[2(x+2)(x-2) = (2x+2+5x-10)/[2(x+2)(x-2)] =

= (7x-8)/[2(x+2)(x-2)]