निम्नलिखित समीकरण को हल कीजिये:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3, (x ne 4, 3)`

Explanation

दी समीकरण
`(2x)/(x-4) +(2x-5)/(x-3)=25/3`
`rArr (2x(x-3)+(x-4)(2x-5))/((x-4)(x-3)) = 25/3`
`rArr (2x^(2)-6x+2x^(2)-5x-8x+20)/(x^(2)-3x-4x+12)=25/3`
`rArr (4x^(2)-19x+20)/(x^(2)-7x+12)=25/3`
`rArr 3(4x^(2)-19x+20)=25(x^(2)-7x+12)`
`rArr 12x^(2)-57x+60 = 25x^(2)-175x+300`
`rArr 25x^(2)-175x+300-12x^(2)+57x-60=0`
`rArr 13x^(2)-118x+240=0`
`rArr 13x^(2)-(78+40)x+240=0`
`rArr 13x^(2)-78x-40x+240=0`
`rArr 13x(x-6)-40(x-6)=0`
`rArr (x-6)(13x-40)=0`
`rArr x-6=0` या `13x-40=0`
`rArr x=6` या `x=40/13`
अतः दिए समीकरण का हल =6 और `40/13`