can some one help me with this problem 3/x+6-1/x-2 = -8/ x2+4x-12 the last step is x to the second?

Question

this the problem 3 over x+3 - 1 over x-2 = -8 over x to the 2 + 4x-12

Answer 1

3/(x + 6) - 1/(x - 2) = -8/(x^2 + 4x -12)

Step 1: Create a common denominator for the left side. This is convenient, because (x + 6) * (x - 2) = (x^2 + 4x - 12)
3/(x + 6) * (x - 2) / (x - 2) - 1/(x - 2) * (x + 6) / (x + 6)
3 (x - 2) / ((x + 6) * (x - 2)) - 1 (x + 6) / ((x + 6) * (x - 2))

Finally:
(3 (x - 2) - 1 (x + 6)) / (x^2 + 4x -12) = -8/(x^2 + 4x -12)

Step 2: Cancel the x^2 + 4x -12 denominator on both sides, then solve.
(3 (x - 2) - 1 (x + 6)) / (x^2 + 4x -12) = -8/(x^2 + 4x -12)
3 (x - 2) - 1 (x + 6) = -8
3x - 6 - x - 6 + 8 = 0
2x - 4 = 0
2x = 4
x = 2 (solution!)

Answer 2

y = x² - 4x - 2 Parabola is in accepted kind ax² + bx + c, the position a = a million, b = - 4, c = - 2 Equation of the axis of symmetry is x = - b/2a = - - 4/2(a million) = 2 it truly is the x-coordinate of the vertex. fixing the function for this cost supplies the y-coordinate. y = 2² - 4(2) - 2 = 4 - 8 - 2 = - 6 Vertex is (2, - 6).