What is the solution set of the equation 2/x - 3x/x+3 = x/x+3

Solving a quadratic equation, and paying attention to the domain, the solution set of the equation is:

The equation given is:

Placing everything on the same side of the equality:

Applying the least common factor:

Then:

In a fraction, the denominator cannot be zero, thus and cannot belong to the solution set.

The solutions are the values of x for which:

Simplifying by -2:

Which is a quadratic equation with coefficients .

Then, applying Bhaskara:

Thus, the solution set is:

A similar problem is given at link

x = -1; x = ³/₂

Step-by-step explanation:

 2/x - 3x/(x + 3) = x/(x+3)     Subtract x/(x+ 3) from each side

 2/x - 4x/(x+ 3)  = 0             Divide each side by 2

  1/x - 2x/(x + 3) = 0             Multiply each side by x(x+ 3)

        x + 3 - 2x² = 0             Multiply each side by -1

        2x² - x - 3 = 0              Factor the quadratic

    (2x - 3)(x + 1) = 0             Find the zeroes

2x - 3 = 0       x + 1 = 0

    2x = 3             x = -1

      x = ³/₂

The solution set is x = -1, x = ³/₂.

The graph shows the x-intercepts at (-1, 0) and (1.5,0) and the vertical asymptotes at x = -3 and x = 0.

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.