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Question

Solution of the equation fraction numerator d y over denominator d x end fraction equals fraction numerator y to the power of 2 end exponent minus y minus 2 over denominator x to the power of 2 end exponent plus 2 x minus 3 end fraction is minus( where c is arbitrary constant)

  1. fraction numerator 1 over denominator 3 end fraction blank l o g blank left parenthesis fraction numerator y minus 2 over denominator y plus 1 end fraction right parenthesis equals fraction numerator 1 over denominator 4 end fraction blank l o g blank left parenthesis fraction numerator x plus 3 over denominator x minus 1 end fraction right parenthesis plus c    
  2. fraction numerator 1 over denominator 3 end fraction blank l o g left parenthesis fraction numerator y plus 1 over denominator y minus 2 end fraction right parenthesis equals fraction numerator 1 over denominator 4 end fraction blank l o g blank left parenthesis fraction numerator x minus 1 over denominator x plus 3 end fraction right parenthesis plus c    
  3. 4 blank l o g blank left parenthesis fraction numerator y minus 2 over denominator y plus 1 end fraction right parenthesis equals 3 blank l o g blank left parenthesis fraction numerator x minus 1 over denominator x plus 3 end fraction right parenthesis plus c    
  4. None of these    

The correct answer is: 4 blank l o g blank left parenthesis fraction numerator y minus 2 over denominator y plus 1 end fraction right parenthesis equals 3 blank l o g blank left parenthesis fraction numerator x minus 1 over denominator x plus 3 end fraction right parenthesis plus c


    not stretchy integral subscript blank superscript blank fraction numerator d y over denominator left parenthesis y minus 2 right parenthesis left parenthesis y plus 1 right parenthesis end fraction equals not stretchy integral subscript blank superscript blank fraction numerator d x over denominator left parenthesis x plus 3 right parenthesis left parenthesis x minus 1 right parenthesis end fraction
    equals 4 blank l o g blank vertical line fraction numerator y minus 2 over denominator y plus 1 end fraction vertical line equals 3 blank l o g blank x vertical line fraction numerator x minus 1 over denominator x plus 3 end fraction vertical line plus c

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