Question

When solving the following equation:

2/(x-5) = 4/(x+1)

explain why we must exclude x = 5 and x = −1 as possible solutions from the solution set.

Answer 1

We need to exclude x = 5 and x = -1 as possible solutions because they result in division by zero.

Step-by-step explanation:

To solve the equation 2/(x-5) = 4/(x+1), we need to determine the values of x that make the equation true. However, we must exclude x = 5 and x = -1 as possible solutions because they would result in a division by zero.

When x = 5, the numerator of the left side of the equation becomes 2/(5-5) = 2/0, which is undefined. Similarly, when x = -1, the numerator of the right side of the equation becomes 4/(-1+1) = 4/0, also undefined.

Therefore, we cannot include x = 5 and x = -1 in the solution set of the equation.