Question

Solve the rational equation: 1/x-1 - 1/x+2 = 1/4

Answer 1

9514 1404 393

Answer:

x = -0.5 ±√14.25

Explanation:

Subtract 1/4 and combine terms.

`(1)/(x-1)-(1)/(x+2)-(1)/(4)=0\\\\(4(x+2)-4(x-1)-(x-1)(x+2))/(4(x-1)(x+2))=0\\\\(-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√(14.25)\qquad\text{add 14.25, square root, subtract 0.5}\\\\x\approx\{-4.2749, 3.2749\}`