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

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.