Identifying the Equation:
To solve the equation \( \frac{a+10}{a+11} = \frac{a+5}{a-10} \), we first need to identify the equation we are working with.

Combining Fractions:
To start solving the equation, we can combine the fractions by finding a common denominator. In this case, the common denominator is \( (a+11)(a-10) \).

Cross Multiplying:
After combining the fractions, we can cross multiply to get rid of the denominators. This will leave us with a quadratic equation that we can solve for 'a'.

Solving the Quadratic Equation:
Once we have the quadratic equation, we can simplify it by expanding and rearranging the terms. This will give us a standard form quadratic equation that we can solve using methods like factoring, completing the square, or using the quadratic formula.

Checking for Extraneous Solutions:
After finding the solutions for 'a', it is important to check for extraneous solutions. This involves plugging the solutions back into the original equation to ensure they are valid.

Final Answer:
Once we have found the valid solutions for 'a' and confirmed their correctness, we can present the final answer to the equation \( \frac{a+10}{a+11} = \frac{a+5}{a-10} \).