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Question
Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`
Solution
`3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3, `
This can be rewritten as:
`3/(x+1)-2/(3x-1)=1/2`
`(3(3x-1)-2(x+1))/((x+1)(3x-1))=1/2`
`(7x-5)/(3x^2+2x-1)=1/2`
On cross multiplying, we get:
2(7x-5)=3x2+2x-1
14x-10=3x2+2x-1
3x2-12x+9=0
3x2-9x-3x+9=0
3x(x-3)-3(x-3)=0
(3x-3)(x-3)=0
3(x-1)(x-3)=0
(x-1)(x-3)=0
x=1,3
Thus, the solution of the given equation is 1 or 3.
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