$\frac{5}{x+2}$-$\frac{x-1}{2-x}$=$\frac{12}{x^2+4}$+1

5/x+2-x-1/2-x=12/x^2+4+x1

<=> 5/x+2-1-x/x-2=12/(x+2)(x-2)+1

<=> 5(x-2)/(x+2)(x-2) - (1-x)(x+2)/(x-2)(x+2)=12/(x+2)(x-2)+(x-2)(x+2)

=> 5(x-2)-(1-x)(x+2)=12+(x-2)(x+2)

<=> 5x-10-x-2+x^2+2x=12+x^2+2x-2x-4

<=> 5x-x+2x-2x+2x+x^2-x^2=12-4+12

<=>  6x=20

<=> x=20/6

<=> x=10/3