2/3 x 1/2 = ?
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ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
Ta có: \(\dfrac{x-3}{x+1}=\dfrac{x^2}{x^2-1}\)
\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}\)
Suy ra: \(x^2-4x+3-x^2=0\)
\(\Leftrightarrow-4x=-3\)
hay \(x=\dfrac{3}{4}\)(thỏa ĐK)
Vậy: \(S=\left\{\dfrac{3}{4}\right\}\)
\(\Leftrightarrow2x\left(x+5\right)-3\left(x-2\right)=7x+1\)
\(\Leftrightarrow2x^2+10x-3x+6-7x-1=0\)
\(\Leftrightarrow2x^2+5=0\)(vô lý)
ĐKXĐ:\(\left\{{}\begin{matrix}x\ne2\\x\ne-5\end{matrix}\right.\)
\(\dfrac{2x}{x-2}-\dfrac{3}{x+5}=\dfrac{7x+1}{x^2+3x-10}\\ \Leftrightarrow\dfrac{2x\left(x+5\right)}{\left(x+5\right)\left(x-2\right)}-\dfrac{3\left(x-2\right)}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x^2-2x+5x-10}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x\left(x-2\right)+5\left(x-2\right)}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}-\dfrac{7x+1}{\left(x+5\right)\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{2x^2+10x-3x+6-7x-1}{\left(x+5\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{2x^2+5}{\left(x+5\right)\left(x-2\right)}=0\\ \Rightarrow2x^2+5=0\left(vô.lí\right)\)
Vậy pt vô nghiệm
1, Ta có :
\(x+\frac{3}{5}=\frac{4}{7}\div\frac{8}{21}\)
\(x+\frac{3}{5}=\frac{4}{7}\times\frac{21}{8}\)
\(x+\frac{3}{5}=\frac{3}{2}\)
\(x=\frac{3}{2}-\frac{3}{5}\)
\(x=\frac{15}{10}-\frac{6}{10}\)
\(x=\frac{9}{10}\)
Vậy x = \(\frac{9}{10}\)
2, Ta có :
\(\frac{2}{3}+\frac{3}{4}\div x=-\frac{1}{6}\)
\(\frac{3}{4}\div x=-\frac{1}{6}-\frac{2}{3}\)
\(\frac{3}{4}\div x=-\frac{1}{6}-\frac{4}{6}\)
\(\frac{3}{4}\div x=-\frac{5}{6}\)
\(x=\frac{3}{4}\div\left(-\frac{5}{6}\right)\)
\(x=\frac{3}{4}\times\left(-\frac{6}{5}\right)\)
\(x=-\frac{9}{10}\)
Vậy x = \(-\frac{9}{10}\)
( x - 1 ) + ( x - 2 ) + ( x - 3 ) = 180
x - 1 + x - 2 + x - 3 = 180
3x - 1 - 2 - 3 = 180
3x - ( 1 + 2 + 3 ) = 180
3x - 6 = 180
3x = 180 + 6
3x = 186
x = 186 : 3
x = 62
2/6 = 1/3
2/3 x 1/2 =2/6=1/3