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Question
`3((7x+1)/(5x-3))-4((5x-3)/(7x+1))=11,x≠3/5,-1/7`
Solution
`3((7x+1)/(5x-3))-4((5x-3)/(7x+1))=11,x≠3/5,-1/7`
⇒`(3(7x+1)^2-4(5x-3)^2)/((5x-3)(7x+1))=11`
⇒`(3(7x+1)^2-4(5x-3)^2)/((5x-3)(7x+1))=11`
⇒`(3(49x^2+14x+1)-4(25x^3-30x+9))/(35x^3-16-3)=11`
⇒`(147x^2+42x+3-100x^2+120x-36)/(35x^2-16x-3)=11`
⇒`(47x^2+162x-33)/(35x^2-16x-3)=11`
⇒`47x^2+162x-33=385x^2-176x-33`
⇒`338x^2-338x=0`
⇒`338x(x-1)=0`
⇒`x=0 or x-1=0`
⇒ `x=0 or x=1`
Hence, 0 and 1 are the roots of the given equation.
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