Question

x+3/x-2 - 1-x/x=17/4

Answer 1

Hey there!

(x+3/x-2) - (1-x/x)=17/4.

(x+3)x-(1-x)(x-2)/ (x-2)x = 17/4

x²+3x-(x-2-x²+3x)/x²-2x=17/4

x²+3x-x+2+x²-3x/x²-2x=17/4

2x²-x+2/x²-2x=17/4

4(2x²-x+2)=17(x²-2x)

8x²-4x+8=17x²-34x

34x-4x+8=17x²-8x²

30x+8=9x²

9x²-30x-8=0

x= -(-30)±√30²-4(9)(8)/2(9)

=+30±√612/18

=30±6√17/18

=6(5±√17)/18

=5±√17/3


Therefore, x=5+√17/3 or 5-√17/3