2 - x = 1/5 : 1/4
3 - x × = 1/3 : 1/6
b )
1/3 × 1/2 + 1/5 × 1/2
37373 phần 414141 : 4545 phần 4141
2727 phần 4242 + 13 phần 42 + 444444 phần 424242
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2 - x = \(\frac{1}{5}\): \(\frac{1}{4}\)
2 -x = \(\frac{4}{5}\)
x = 2 - \(\frac{4}{5}\)
x = \(\frac{6}{5}\)
3 - x \(\times\) \(\frac{1}{3}\)= \(\frac{1}{6}\) \(\Rightarrow\) 3 - x = \(\frac{1}{6}\) \(\div\frac{1}{3}\)
3 - x = \(\frac{1}{2}\) \(\Rightarrow\) x = 3 - \(\frac{1}{2}\) \(\Rightarrow\) x = \(\frac{5}{2}\)
\(\frac{5}{6}=\frac{x-1}{x}\left(đk:x\ne0\right)\)
\(< =>5x=6\left(x-1\right)< =>5x=6x-6\)
\(< =>6x-5x=6< =>x=6\left(tmđk\right)\)
\(\frac{1}{2}=\frac{x+1}{3x}\left(đk:x\ne0\right)\)
\(< =>3x=2\left(x+1\right)< =>3x=2x+2\)
\(< =>3x-2x=2< =>x=2\left(tmđk\right)\)
\(\frac{3}{x+2}=\frac{5}{2x+1}\left(đk:x\ne-2;-\frac{1}{2}\right)\)
\(< =>3\left(2x+1\right)=5\left(x+2\right)< =>6x+3=5x+10\)
\(< =>6x-5x=10-3< =>x=7\left(tmđk\right)\)
\(\frac{5}{8x-2}=-\frac{4}{7-x}\left(đk:x\ne\frac{1}{4};7\right)\)
\(< =>\frac{5}{8x-2}=\frac{4}{x-7}< =>5\left(x-7\right)=4\left(8x-2\right)\)
\(< =>5x-35=32x-8< =>32x-5x=-35+8\)
\(< =>27x=-27< =>x=-1\)
\(\frac{4}{3}=\frac{2x-1}{3}< =>4.3=\left(2x-1\right).3\)
\(< =>12=6x-3< =>6x=12+3\)
\(< =>6x=15< =>x=\frac{15}{6}=\frac{5}{2}\)
\(\frac{2x-1}{3}=\frac{3x+1}{4}< =>4\left(2x-1\right)=3\left(3x+1\right)\)
\(< =>8x-4=9x+3< =>9x-8x=-4-3\)
\(< =>9x-8x=-7< =>x=-7\)
\(\frac{4}{x+2}=\frac{7}{3x+1}\left(đk:x\ne-2;-\frac{1}{3}\right)\)
\(< =>4\left(3x+1\right)=7\left(x+2\right)< =>12x+4=7x+14\)
\(< =>12x-7x=14-4< =>5x=10\)
\(< =>x=\frac{10}{5}=2\left(tmđk\right)\)
\(-\frac{3}{x+1}=\frac{4}{2-2x}\left(đk:x\ne-1;1\right)\)
\(< =>-3\left(2-2x\right)=4\left(x+1\right)< =>-6+6x=4x+4\)
\(< =>6x-4x=4+6< =>2x=10\)
\(< =>x=\frac{10}{2}=5\left(tmđk\right)\)
\(\frac{x+1}{3}=\frac{3}{x+1}\left(đk:x\ne-1\right)\)
\(< =>\left(x+1\right)\left(x+1\right)=3.3\)
\(< =>x^2+2x+1=9< =>x^2+2x+1-9=0\)
\(< =>x^2+2x-8=0< =>x^2-2x+4x-8=0\)
\(< =>x\left(x-2\right)+4\left(x-2\right)=0< =>\left(x+4\right)\left(x-2\right)=0\)
\(< =>\orbr{\begin{cases}x+4=0\\x-2=0\end{cases}< =>\orbr{\begin{cases}x=-4\\x=2\end{cases}}}\left(tmđk\right)\)
2 - x = 1/5 : 1/4
2 - x = 1/5 * 4
2 - x = 4/5
x = 2 - 4/5
x = 6/5
3 - x = 1/3 : 1/6
3 - x = 1/3 * 6
3 - x = 2
x = 3 - 2
x = 1
b) 1/3 * 1/2 + 1/5 * 1/2
= 1/2 * (1/3 + 1/5)
= 1/2 * 8/15
= 4/15
373737/414141 : 4545/4141
= 37/41 : 45/41
= 37/41 * 41/45
= 37/45
2727/4242 + 13/42 + 444444/424242
= 9/14 + 13/42 + 22/21
= 2