9514 1404 393
Answer:
x = -0.5 ±√14.25
Step-by-step explanation:
Subtract 1/4 and combine terms.
[tex]\dfrac{1}{x-1}-\dfrac{1}{x+2}-\dfrac{1}{4}=0\\\\\dfrac{4(x+2)-4(x-1)-(x-1)(x+2)}{4(x-1)(x+2)}=0\\\\\dfrac{-x^2-x+14}{4(x-1)(x+2)}=0\\\\x^2 +x -14=0\qquad\text{no factors cancel, numerator must be zero}\\\\(x+0.5)^2-14.25=0\qquad\text{complete the square}\\\\x=-0.5\pm\sqrt{14.25}\qquad\text{add 14.25, square root, subtract 0.5}\\\\x\approx\{-4.2749, 3.2749\}[/tex]
