2x x 3x answer
Asked by maham237 @ in Mathematics viewed by 291 People
What is the solution set of the equation 2/x - 3x/x+3 = x/x+3
Answered by maham237 @
Answer:
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.
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