Toán Lớp 8: giải phg trình
$\frac{x-1}{13}$- $\frac{2x-3}{15}$= $\frac{3x-15}{27}$- $\frac{4x-27}{29}$
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Toán Lớp 8: giải phg trình
$\frac{x-1}{13}$- $\frac{2x-3}{15}$= $\frac{3x-15}{27}$- $\frac{4x-27}{29}$
Comments ( 1 )
Giải đáp:$x = 14$
Lời giải và giải thích chi tiết:
$\begin{array}{l}
\dfrac{{x – 1}}{{13}} – \dfrac{{2x – 13}}{{15}} = \dfrac{{3x – 15}}{{27}} – \dfrac{{4x – 27}}{{29}}\\
\Leftrightarrow \dfrac{{x – 1}}{{13}} – 1 – \dfrac{{2x – 13}}{{15}} + 1\\
= \dfrac{{3x – 15}}{{27}} – 1 – \dfrac{{4x – 27}}{{29}} + 1\\
\Leftrightarrow \dfrac{{x – 14}}{{13}} – \dfrac{{2x – 13 – 15}}{{15}}\\
= \dfrac{{3x – 15 – 27}}{{27}} – \dfrac{{4x – 27 – 29}}{{29}}\\
\Leftrightarrow \dfrac{{x – 14}}{{13}} – \dfrac{{2x – 28}}{{15}} = \dfrac{{3x – 42}}{{27}} – \dfrac{{4x – 56}}{{29}}\\
\Leftrightarrow \left( {x – 14} \right).\left( {\dfrac{1}{{13}} – \dfrac{2}{{15}} – \dfrac{3}{{27}} + \dfrac{4}{{29}}} \right) = 0\\
\Leftrightarrow x – 14 = 0\\
\Leftrightarrow x = 14\\
Vậy\,x = 14
\end{array}$