Question

Solve : 1 / (x−1) – 1/x = 1 / (x+3) – 1/(x+4)​

Answer 1

Answer:

taking both side L.C.M.

x-(x-1)/(x-1)x= (x+4)-(x+3)/(x+3)(x+4)

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

x^2+4x+3x+12=x^2-x

7x+x+12=0

8x=-12

x=-3/2

Answer 2

Answer:

$x=\frac{-3}{2}$

Step-by-step explanation:

$\frac{1}{x-1} - \frac{1}{x} = \frac{1}{x+3} - \frac{1}{x+4}\\\frac{x-(x-1)}{x(x-1)} = \frac{(x+4)-(x+3)}{(x+3)(x+4)}\\\frac{x-x+1}{x^2-x} = \frac{x+4-x-3}{x^2+4x+3x+12}\\\frac{1}{x^2-x} = \frac{1}{x^2+7x+12}\\x^2+7x+12 = x^2-x\\8x+12 = 0\\8x = -12\\x = \frac{-12}{8}\\x=\frac{-3}{2}$