\(\dfrac{140}{x}-\dfrac{140}{x-6}=\dfrac{-1}{6}\)

\(\Leftrightarrow\dfrac{140\left(x-6\right)-140x}{x\left(x-6\right)}=-\dfrac{1}{6}\)

\(\Leftrightarrow\dfrac{-840}{x\left(x-6\right)}=-\dfrac{1}{6}\)

\(\Leftrightarrow x^2-6x-5040=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=74.05\\x=-68.05\end{matrix}\right.\)

Lời giải:

\(\frac{140}{x}-\frac{140}{x-6}=\frac{-1}{6}\Leftrightarrow \frac{140(x-6-x)}{x(x-6)}=\frac{-1}{6}\)

\(\Leftrightarrow x(x-6)=5040\Leftrightarrow x^2-6x-5040=0\)

\(\Leftrightarrow (x-3)^2-5049=0\)

\(\Leftrightarrow (x-3-\sqrt{5049})(x-3+\sqrt{5049})=0\Rightarrow x=3\pm \sqrt{5049}\)

\(1,\dfrac{3x+2}{6}-\dfrac{3x-2}{4}=\dfrac{15}{8}\\ \Leftrightarrow\dfrac{4\left(3x+2\right)}{24}-\dfrac{6\left(3x-2\right)}{24}-\dfrac{45}{24}=0\\ \Leftrightarrow12x+24-18x+12-45=0\\ \Leftrightarrow-6x-9=0\\ \Leftrightarrow x=-\dfrac{3}{2}\)

2, ĐKXĐ:\(x\ne\pm3\)

\(\dfrac{x+2}{3+x}-\dfrac{x}{3-x}=\dfrac{8x-6}{9-x^2}\\ \Leftrightarrow\dfrac{\left(x+2\right)\left(3-x\right)}{\left(3+x\right)\left(3-x\right)}-\dfrac{x\left(3+x\right)}{\left(3+x\right)\left(3-x\right)}-\dfrac{8x-6}{\left(3+x\right)\left(3-x\right)}=0\\ \Leftrightarrow\dfrac{-x^2+x+6-3x-x^2-8x+6}{\left(3+x\right)\left(3-x\right)}=0\\ \Leftrightarrow-2x^2-10x+12=0\\ \Leftrightarrow x^2+5x-6=0\\ \Leftrightarrow\left(x-1\right)\left(x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-6\left(tm\right)\end{matrix}\right.\)

\(a,\dfrac{3x+2}{6}-\dfrac{3x-2}{4}=\dfrac{15}{8}\)

\(\Leftrightarrow4\left(3x+2\right)-6\left(3x-2\right)=45\)

\(\Leftrightarrow12x+8-18x+12=45\)

\(\Leftrightarrow12x-18x=45-12-8\)

\(\Leftrightarrow-6x=25\)

\(\Leftrightarrow x=\dfrac{-25}{6}\)

Vậy \(S=\left\{\dfrac{-25}{6}\right\}\)

\(b,\dfrac{x+2}{3+x}-\dfrac{x}{3-x}=\dfrac{8x-6}{9-x^2}\left(ĐKXĐ:x\ne3;x\ne-3\right)\)

\(\Leftrightarrow\left(x+2\right)\left(3-x\right)-x\left(3+x\right)=8x-6\)

\(\Leftrightarrow3x-x^2+6-2x-3x-x^2=8x-6\)

\(\Leftrightarrow-x^2-x^2+3x-2x-3x-8x=-6+6\)

\(\Leftrightarrow-2x^2-10x=0\)

\(\Leftrightarrow-2x\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-2x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(nhận\right)\\x=5\left(nhận\right)\end{matrix}\right.\)

Vậy \(S=\left\{0;5\right\}\)

câu 1= 13288

câu 2= 14368

câu 1= 13288

câu 2=14368

chúc bạn học giỏi

1-2+3-4+5-6+............+45-46+47-48+100

= (1-2)+(3-4)+(5-6)+............+(45-46)+(47-48)+100

=  (-1) + (-1) + (-1)+ ...............+(-1)+(-1) +100 ( có 24 cặp -1)

=(-1)x24+100

=( -24) +100

=76

Nhớ k cho mk nha! ^-^