Solve for $\mathrm{X}: \frac{(x-6)(x+1)}{x+1}=0$

Step 1 ：The given equation is a rational equation: \(\frac{(x-6)(x+1)}{x+1}=0\).

Step 2 ：To solve for x, we need to set the numerator equal to zero because a fraction is equal to zero if and only if its numerator is zero. The denominator cannot be zero because division by zero is undefined in mathematics.

Step 3 ：Therefore, we need to solve the equation \((x-6)(x+1) = 0\). This equation can be solved by setting each factor equal to zero and solving for x.

Step 4 ：The solutions to the equation are \(x = -1\) and \(x = 6\).

Step 5 ：However, we need to check if these solutions are valid. A solution is invalid if it makes the denominator of the original equation zero.

Step 6 ：In this case, \(x = -1\) makes the denominator zero, so it is not a valid solution.

Step 7 ：Therefore, the only valid solution is \(x = 6\).

Step 8 ：Final Answer: \(\boxed{6}\)