Question

Solving for x, please help

Answer 1

x = 5,-2

Explanation:

Multiply the whole equation by 3(x+1) to get rid of the denominator.

`\large{ (x + 2)/(3) * 3(x + 1) = (2(x + 2))/(x + 1) * 3(x + 1)} \\ \large{(x + 2)(x + 1) = 2(x + 2) * 3} \\ \large{ {x}^(2) + 3x + 2 = 6(x + 2)} \\ \large{ {x}^(2) + 3x + 2 = 6x + 12}`

Then we solve the equation.

`\large{ {x}^(2) + 3x + 2 - 6x - 12 = 0} \\ \large{ {x}^(2) - 3x - 10 = 0} \\ \large{(x - 5)(x + 2) = 0} \\ \large{x = 5, - 2}`

Since we are also solving rational equation, make sure that x ≠ -1 for this problem. Because if x = -1, the denominator is 0 which is undefined. Since our solutions are x = 5,-2 and not -1. Therefore the answer is x = 5,-2