* Giải phương trình : $\frac{x-1}{13}$ – $\frac{2x-13}{15}$ = $\frac{3x-15}{27}$ – $\frac{4x-27}{29}$

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1. Đáp án:

   `S=\{14\}`

   Giải thích các bước giải:

   `\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}`

   `<=>\frac{x-1}{13}-\frac{2x-13}{15}-1+1=\frac{3x-15}{27}-\frac{4x-27}{29}-1+1`

   `<=>(\frac{x-1}{13}-1)-(\frac{2x-13}{15}-1)=(\frac{3x-15}{27}-1)-(\frac{4x-27}{29}-1)`

   `<=>\frac{x-1-13}{13}-\frac{2x-13-15}{15}=\frac{3x-15-27}{27}-\frac{4x-27-29}{29}`

   `<=>\frac{x-14}{13}-\frac{2(x-14)}{15}=\frac{3(x-14)}{27}-\frac{4(x-14)}{29}`

   `<=>\frac{x-14}{13}-\frac{2(x-14)}{15}-\frac{3(x-14)}{27}+\frac{4(x-14)}{29}=0`

   `<=>(x-14)(1/13-2/15-3/27+4/29)=0`

   `<=>x-14=0(`Do`1/13-2/15-3/27+4/29\ne 0)`

   `<=>x=14`

    Vậy `S=\{14\}`

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2. $\begin{array}{l}
   \dfrac{{x – 1}}{{13}} – \dfrac{{2x – 13}}{{15}} = \dfrac{{3x – 15}}{{27}} – \dfrac{{4x – 27}}{{29}}\\
    \Leftrightarrow \left( {\dfrac{{x – 1}}{{13}} – 1} \right) – \left( {\dfrac{{2x – 13}}{{15}} – 1} \right) = \left( {\dfrac{{3x – 15}}{{27}} – 1} \right) – \left( {\dfrac{{4x – 27}}{{29}} – 1} \right)\\
    \Leftrightarrow \dfrac{{x – 14}}{{13}} – \dfrac{{2\left( {x – 14} \right)}}{{15}} – \dfrac{{3\left( {x – 14} \right)}}{{27}} + \dfrac{{4\left( {x – 14} \right)}}{{29}} = 0\\
    \Leftrightarrow \left( {x – 14} \right)\left( {\underbrace {\dfrac{1}{{13}} – \dfrac{2}{{15}} – \dfrac{3}{{27}} + \dfrac{4}{{29}}}_{ < 0}} \right) = 0\\
    \Leftrightarrow x = 14
   \end{array}$

    

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