Question:সরল কর: 

 ৫. ঝ.` 1/(a - b - c) + 1/(a - b + c) + a/(a^2 + b^2 - c^2 - 2ab)`

    ঞ. `1/(a^2 + b^2 - c^2 + 2ab) + 1/(b^2 + c^2 - a^2 + 2bc) + 1/(c^2 + a^2 - b^2 + 2ca)` 

Answer ঝ.` 1/(a - b - c) + 1/(a - b + c) + a/(a^2 + b^2 - c^2 - 2ab)`

     `= (a - b + c + a - b - c)/((a - b - c) (a - b + c)) + a/(a^2 + b^2 - c^2 - 2ab)`

     `= (2a - 2b)/((a - b)^2 - c^2) + a/(a^2 + b^2 - c^2 - 2ab)`

     `= (2a - 2b)/(a^2 - 2ab + b^2 - c^2) + a/(a^2 + b^2 - c^2 - 2ab)`

     `= (2a - 2b + a)/(a^2 - 2ab + b^2 + c^2)`

     `= (3a - 2b)/(a^2 + b^2 - c^2 - 2ab)`

       উত্তর: ` (3a - 2b)/(a^2 + b^2 - c^2 - 2ab)`


  ঞ. `1/(a^2 + b^2 - c^2 + 2ab) + 1/(b^2 + c^2 - a^2 + 2bc) + 1/(c^2 + a^2 - b^2 + 2ca)`

    `= 1/((a^2 + + 2ab + b^2) - c^2)  + 1/((b^2 + 2bc + c^2) - a^2) `

           `+ 1/((c^2 + 2ca + a^2) - b^2)`

    `= 1/((a + b)^2 - c^2) + 1/((b + c)^2 - a^2) + 1/((c + a)^2 - b^2)`

    `= 1/((a + b + c) (a + b - c)) + 1/((b + c + a) (b + c - a)) `

            `+ 1/((c + a + b) (c + a - b))`

    `= ((b + c - a) (c + a - b) + (a + b - c) (c + a - b) + (a + b - c) (b + c - a))/((a + b + c) (a + b - c) (b + c - a) (c + a - b))`

  এখন লব, =

      `bc + ab - b^2 + c^2 + ca - bc - ca - a^2 + ab + ca + a^2 - ab + bc + ab `
                       
           `- b^2 - c^2 - ca + bc + ab + ca - a^2 + b^2 + bc - ab - bc - c^2 + ca`

      `= 2ca + 2bc + 2ab - b^2 - c^2 - a^2`

     `= 2ab + 2bc + 2ca - a^2 - b^2 - c^2`

   :. প্রদত্ত রাশি = `(2ab + 2bc + 2ca - a^2 - b^2 - c^2)/((a + b + c) (a + b - c) (b + c - a) (c + a - b))`

    উত্তর: `(2ab + 2bc + 2ca - a^2 - b^2 - c^2)/((a + b + c) (a + b - c) (b + c - a) (c + a - b))` 

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