Solve quadratic equation xx+1+x+1x=2512 (x≠0 and x≠−1).
Answer:
x=3, or x=−4
- On adding two fractions on LHS,
x2+(x+1)2x(x+1)=2512⟹x2+(x2+2x+1)x(x+1)=2512 - 12(2x2+2x+1)=25(x2+x)⟹24x2+24x+12=25x2+25x⟹25x2+25x−24x2−24x−12=0⟹x2+x−12=0⟹x2+4x−3x−12=0⟹x(x+4)−3(x+4)=0⟹(x−3)(x+4)⟹x=3 or −4
- Hence, x=3, or x=−4.