2 ( x - 1 / x + 3 ) - 7 ( x + 3 / x - 1 ) = 5
Solution:
Get the LCD:
( 7 ( x - 1 / x + 3 ) - 2 ( x + 3 / x - 1 ) ) / 14 = 15
( 7 ( x + 3 ) - 2 ( x - 1 ) / ( x + 3 ) ( x - 1 ) ) / 14 = 15
7 ( x + 3 ) - 2 ( x - 1 ) / ( x + 3 ) ( x - 1 ) = 210
( 7x + 21 - 2x + 2 ) / ( x + 3 ) ( x - 1 ) = 210
( 5x + 23 ) / ( x + 3 ) ( x - 1 ) = 210
5x + 23 = 210 ( x + 3 ) ( x - 1 )
5x + 23 = 210 ( x^2 + 2x - 3 )
5x + 23 = 210x^2 + 420x - 330
210x^2 + 420x - 5x = 330 - 23
210x^2 + 415x - 307 = 0
The answer would be 210x^2 + 415x - 307 = 0.