The equation has no quadratic terms so it is a rational algebraic equation. To be able to transform it can be simply simplified:
1/x + 1/1+x = 7/12 First find the LCD and multiply it to each term (LCD=12x+12x²)
(12+12x) + 12x = 7x+7x² Transpose the equation in the right side to the left side and combine the similar terms in the left side.
12+17x-7x²=0 Multiply it to -1 so that the quadratic term is positive and arrange the terms
x = 3 and -4/7