1/x (x+2) + 1 / (x+1) ²=7/12

1 / (x²+2x) + 1 / (x²+2x+1) = 7/12

x²+2x=a

1/a + 1 / (a+1) = 7/12

12 (a+1+a) = 7a (a+1)

7a²-17a-12=0

D=289+336=625

a1 = (17-25) / 14=-4/7⇒x²+2x=-4/7

7x²+14x+4=0

D=196-112=84

x1 = (-14-2√21) / 14=-1-√21/7

x2=-1+√21/7

a2 = (17+25) / 14=8/7⇒x²+2x=8/7

7x²+14x-8=0

D=196+224=420

x3 = (-14-2√105) / 14=-1-√105/7

x4=-1+√105/7