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Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
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Solution
`2/(x+1)+3/(2(x-2))=23/(5x)`
`=>(4(x-2)+3(x+1))/(2(x+1)(x-2))=23/(5x)`
`=>(7x-5)/(2(x^2-x-2))=23/(5x)`
⇒5x(7x−5)=46(x2−x−2)
⇒11x2−21x−92=0
⇒11x2−44x+23x−92=0
⇒11x(x−4)+23(x−4)=0
⇒(11x+23)(x−4)=0
`=>x = -23/11,4`
Concept: Solutions of Quadratic Equations by Factorization
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