Question

Find the solution for the rational equation (2/(x + 1) - 5/2x) = 2.

a) x = -1
b) x = 0
c) x = 1
d) x = 2

Answer 1

To solve the rational equation (2/(x + 1) - 5/2x) = 2, follow these steps: find a common denominator, combine like terms, eliminate the denominator, simplify the equation, rearrange into a quadratic equation, and use the quadratic formula to solve for x. The solutions are x = -1 and x = 0.5.

Step-by-step explanation:

To solve the rational equation (2/(x + 1) - 5/2x) = 2, we need to find the value of x. Here are the steps:

1. Combine the fractions on the left side of the equation by finding a common denominator. The common denominator is 2x(x + 1).
2. Multiply each fraction by the necessary factors to get a common denominator. This results in the equation (4x - 5(x + 1))/(2x(x + 1)) = 2.
3. Combine like terms and simplify the equation further. You should have (4x - 5x - 5)/(2x(x + 1)) = 2, which simplifies to (-x - 5)/(2x(x + 1)) = 2.
4. Cross multiply to eliminate the denominator. This gives you the equation -x - 5 = 4x(x + 1).
5. Distribute the 4x on the right side and collect like terms. You should have the quadratic equation 4x² + 4x - x - 5 = 0.
6. Simplify and rearrange the equation to 4x² + 3x - 5 = 0.
7. Use the quadratic formula to solve for x. In this case, the solutions are approximately x = -1 and x = 0.5.

So, the solution for the rational equation is x = -1 and x = 0.5 (option a).