Answer
$$x=3$$
Work Step by Step
$$\frac{3}{(x+2)(x-1)}-\frac{1}{(x+1)(x-1)}=\frac{7}{2(x+2)(x+1)}$$
$$(2(x+2)(x+1)(x-1))(\frac{3}{(x+2)(x-1)}-\frac{1}{(x+1)(x-1)})=(2(x+2)(x+1)(x-1))(\frac{7}{2(x+2)(x+1)})$$
$$6(x+1)-2(x+2)=7(x-1)$$
$$6x+6-2x-4=7x-7$$
$$4x+2=7x-7$$
$$-3x=-9$$
$$x=3$$