Find x: (x+3/x-2) - (1-x/x)=17/4.
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32
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
(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
kinkyMkye:
3rd step....is incorrect-(x-2-x²+3x) should be -(x-2-x²+2x)
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29
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