10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer 16) Solve for \[x:\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}=\frac{2}{3},x\ne 1,2,3\]

    Answer:

    We have,
    \[\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}=\frac{2}{3},x\ne 1,2,3\]
    \[3(x-3)+3(x-1)=2(x-1)(x-2)(x-3)\]
       \[3x-9+3x-3=2(x-1)(x-2)(x-3)\]
                  \[6x-12=2(x-1)(x-2)()x-3\]
                  \[6(x-2)=2(x-1)(x-2)(x-3)\]
                           \[3=(x-1)(x-3)\]
                           \[3={{x}^{2}}-3x-x+3\]
                 \[{{x}^{2}}-4x=0\]
                 \[x(x-4)=0\]
    \[\therefore \]                               \[x=0\] or \[4\]


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