Tính (rút gọn): a, 1/(x+3)(x+4) + 1/(x+4)(x+5) + 1/(x+5)(x+6). b, 1/(x-2)(x-3) + 1/(x-3)(x-4) + 1/(x-4)(x-5)

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1. Đáp án:

   $\begin{array}{l}
   a)\frac{1}{{\left( {x + 3} \right)\left( {x + 4} \right)}} + \frac{1}{{\left( {x + 4} \right)\left( {x + 5} \right)}} + \frac{1}{{\left( {x + 5} \right)\left( {x + 6} \right)}}\\
    = \frac{{\left( {x + 4} \right) – \left( {x + 3} \right)}}{{\left( {x + 3} \right)\left( {x + 4} \right)}} + \frac{{\left( {x + 5} \right) – \left( {x + 4} \right)}}{{\left( {x + 4} \right)\left( {x + 5} \right)}} + \frac{{\left( {x + 6} \right) – \left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 6} \right)}}\\
    = \frac{1}{{x + 3}} – \frac{1}{{x + 4}} + \frac{1}{{x + 4}} – \frac{1}{{x + 5}} + \frac{1}{{x + 5}} – \frac{1}{{x + 6}}\\
    = \frac{1}{{x + 3}} – \frac{1}{{x + 6}}\\
    = \frac{3}{{\left( {x + 3} \right)\left( {x + 6} \right)}}
   \end{array}$

   b) Tương tự

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2. Đáp án:

    

   Giải thích các bước giải:

    b) 1/(x-2)(x-3) + 1/(x-3)(x-4) + 1/(x-4)(x-5)

   <=> ( x- 4 ) ( x- 5 ) + ( x – 2 ) ( x- 5 ) + ( x- 2 ) ( x- 3 ) / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 ) 

   <=> x^2 – 5x – 4x + 20 + x^2 – 5x – 2x + 10 + x^2 -3x – 2x + 6 / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=> 3x^2 – 21x + 36 / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=>  3 ( x^2 – 7x + 12 ) / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=>  3 ( x^2 – 3x – 4x + 12 ) / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=> 3 [ x ( x – 3 ) – 4 ( x – 3 ) ] / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=> 3 ( x – 3 ) ( x- 4 ) / ( x – 2 ) ( x – 3 ) ( x – 4 ) ( x- 5 )

   <=> 3 / ( x- 2 ) ( x- 5 ) 

   <=> 3 / x^2 – 5x – 2x + 10

   <=> 3 / x^2 – 7x + 10

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