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Question
`3((3x-1)/(2x+3))-2((2x+3)/(3x-1))=5,x≠1/3,-3/2`
Solution
`3((3x-1)/(2x+3))-2((2x+3)/(3x-1))=5,x≠1/3,-3/2`
⇒`(3(3x-1)^2-2(2x+3)^2)/((2x+3)(3x-1))=5`
⇒`(3(9x^2-6x+1)-2(4x^2+12x+9))/(6x^2+7x-3)=5`
⇒`(27x^2-18x+3-8x^2-24x-18)/(6x^2+7x-3)=5`
⇒`(19x^2-42x-15)/(6x^2+7x-3)=5`
⇒`19x^2-42x-15=30x^2+35x-15`
⇒`11x^2+77x=0`
⇒`11x(x+7)=0 `
⇒`x=0 or x+7=0`
⇒ `x=0 or x=-7 `
Hence, 0 and -7 are the roots of the given equation.
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