Question

solve: x + 2/x + 3 + 3/x - 3 = 3

Answer 1

To solve this equation, we need to combine the terms involving "x" on one side and the constant terms on the other side.

Given equation: x + 2/x + 3 + 3/x - 3 = 3

Rearranging the terms:
x + 3 + 3 - 3 + 2/x + 3/x = 3
x + 3 + 2/x + 3/x = 3

Combining the terms involving "x":
(x^2 + 3x) / x + (2 + 3x) / x = 3

Multiplying through by "x" to clear the fractions:
(x^2 + 3x) + (2 + 3x) = 3x
x^2 + 3x + 2 + 3x = 3x
x^2 + 6x + 2 = 3x

Rearranging the terms:
x^2 + 6x - 3x + 2 = 0
x^2 + 3x + 2 = 0

Now, we have a quadratic equation in the form ax^2 + bx + c = 0. We can factor it or use the quadratic formula to solve for "x".

Factoring the quadratic equation:
(x + 2)(x + 1) = 0

Setting each factor to zero and solving for "x":
x + 2 = 0 or x + 1 = 0
x = -2 x = -1

Therefore, the solutions to the equation are x = -2 and x = -1.