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Question
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Solution
`1/(2x-3)+1/(x+5)=1`
`rArr ((x-5)+(2x-3))/((2x-3)(x-5))=1`
`rArr 3x-8=(2x-3)(x-5)`
`rArr 3x-8=2x^2-10x-3x+15`
`rArr 3x-8=2x^2-13x+15`
`rArr 2x^2-16x+23=0`
`∴ x=(-(-16)+-sqrt(-16)^2-4xx2xx23)/(2xx2)`
`=(16+-sqrt256-184)/4`
`=(16+-sqrt2)/4`
`=(16+-6sqrt2)/4`
`=(2(8+-3sqrt2))/4`
`=1/2(8+3sqrt2) or ` `1/2(8-3sqrt2)`
`∴x=1/2(x+3sqrt2)or1/2(8-3sqrt2)`
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