e) (x-1)/x – 1/(x+1)= (2x-1)/(x^2+x) f) 3/(2x-16) + (3x-20)/(x-8) +1/8 =(13x-102)/(3x-24) giúp mk nha please 06/12/2021 Bởi Abigail e) (x-1)/x – 1/(x+1)= (2x-1)/(x^2+x) f) 3/(2x-16) + (3x-20)/(x-8) +1/8 =(13x-102)/(3x-24) giúp mk nha please
Đáp án: $e) x=2\\f) x=12$ Giải thích các bước giải: $e) \frac{x-1}{x}-\frac{1}{x+1}=\frac{2x-1}{x^2+x}\\ĐK: {\left\{\begin{aligned}x\neq 0\\x+1\neq 0\end{aligned}\right.}\Leftrightarrow {\left\{\begin{aligned}x\neq 0\\x\neq -1\end{aligned}\right.}\\\Rightarrow \frac{(x+1)(x-1)}{x(x+1)}-\frac{x}{x(x+1)}=\frac{2x-1}{x^2+x}\\\Leftrightarrow x^2-1=2x-1\\\Leftrightarrow x^2-2x=0\\\Leftrightarrow x(x-2)=0\\\Leftrightarrow {\left[\begin{aligned}x=0(KTĐK)\\x-2=0\end{aligned}\right.}\\\Leftrightarrow x=2\\f) \frac{3}{2x-16}+\frac{3x-20}{x-8}+\frac{1}{8}=\frac{13x-102}{3x-24}\\ĐK: x-8 \neq 0 \Leftrightarrow x\neq 8\\\Rightarrow \frac{36}{24(x-8)}+\frac{24(3x-20)}{24(x-8)}+\frac{3(x-8)}{24(x-8)}=\frac{8(13x-102)}{24(x-8)}\\\Leftrightarrow 36+72x-480+3x-24=104x-816\\\Leftrightarrow 75x-468-104x+816=0\\\Leftrightarrow -29x+348=0\\\Leftrightarrow x=12$ Bình luận
Đáp án:
$e) x=2\\
f) x=12$
Giải thích các bước giải:
$e) \frac{x-1}{x}-\frac{1}{x+1}=\frac{2x-1}{x^2+x}\\
ĐK: {\left\{\begin{aligned}x\neq 0\\x+1\neq 0\end{aligned}\right.}\Leftrightarrow {\left\{\begin{aligned}x\neq 0\\x\neq -1\end{aligned}\right.}\\
\Rightarrow \frac{(x+1)(x-1)}{x(x+1)}-\frac{x}{x(x+1)}=\frac{2x-1}{x^2+x}\\
\Leftrightarrow x^2-1=2x-1\\
\Leftrightarrow x^2-2x=0\\
\Leftrightarrow x(x-2)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0(KTĐK)\\x-2=0\end{aligned}\right.}\\
\Leftrightarrow x=2\\
f) \frac{3}{2x-16}+\frac{3x-20}{x-8}+\frac{1}{8}=\frac{13x-102}{3x-24}\\
ĐK: x-8 \neq 0 \Leftrightarrow x\neq 8\\
\Rightarrow \frac{36}{24(x-8)}+\frac{24(3x-20)}{24(x-8)}+\frac{3(x-8)}{24(x-8)}=\frac{8(13x-102)}{24(x-8)}\\
\Leftrightarrow 36+72x-480+3x-24=104x-816\\
\Leftrightarrow 75x-468-104x+816=0\\
\Leftrightarrow -29x+348=0\\
\Leftrightarrow x=12$