Final answer:
To solve the equation (x + 1)(2x + 4)(1/x - 1) = (x + 1)(1 - 5/2x - 4), cancel the common factor (x + 1), simplify the equation, and then substitute the values from the options to find the solution, using the quadratic formula if necessary.
Step-by-step explanation:
The equation given is (x + 1)(2x + 4)(1/x - 1) = (x + 1)(1 - 5/2x - 4). To solve this equation, we first look for common factors on both sides. We can see that (x + 1) is a common factor and can be cancelled out as long as x ≠ -1. After cancelling (x + 1), the equation simplifies to (2x + 4)(1/x - 1) = 1 - 5/2x - 4.
Next, we might want to clear the fraction by multiplying through by x, which is also allowed as long as x ≠ 0. After multiplying through by x and arranging in the form of a quadratic equation ax^2 + bx + c = 0, we could use the quadratic formula to solve for x. However, without having to expand and solve the quadratic equation, we can check the options given to see which one is a valid solution by substituting the values of x back into the simplified equation.
Upon substitution, we need to discard any values that result in division by zero or are not satisfying the equation after simplification. The remaining value would be the solution.