The equation in the image is:

$\frac{1}{x(x+2)} - \frac{1}{(x+1)^2} = \frac{1}{12}.$

Solution:

Step 1: Find a common denominator

The denominators in the equation are $x(x+2)$, $(x+1)^2$, and $12$. The least common denominator (LCD) for these is:

$\text{LCD} = 12 \cdot x(x+2)(x+1)^2.$

Step 2: Rewrite the equation with the LCD

Multiply through by the LCD to eliminate the fractions:

$\text{LCD} \cdot \frac{1}{x(x+2)} - \text{LCD} \cdot \frac{1}{(x+1)^2} = \text{LCD} \cdot \frac{1}{12}.$

This simplifies to:

$\frac{12(x+1)^2}{x(x+2)} - \frac{12x(x+2)}{(x+1)^2} = x(x+2)(x+1)^2.$

Step 3: Combine and simplify

To simplify further, expand the terms, combine like terms, and solve for $x$. Would you like a detailed step-by-step simplification and solution?