1/x(x+2)+1/(x+1)²=7/12

Question

1/x(x+2)+1/(x+1)²=7/12

Answer 1

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