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X-1/x+2=x-2/x+3
=>(x-1)(x+3)=(x+2)(x-2)
=>x(x+3)-1(x+3)=x(x-2)+2(x-2)
=>x^2+3x-x-3=x^2-2x+2x-4
=>x^2+2x-3=x^2-4
=>2x-3=-4=>x=-1/2=-0,5
vậy...
\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\)
\(\Leftrightarrow x^2-x+3x-3=x^2-2x+2x-4\)
\(\Leftrightarrow x^2+2x-3=x^2-4\)
\(\Leftrightarrow x^2-x^2+2x=3-4\)
\(\Leftrightarrow2x=-1\Leftrightarrow x=-\frac{1}{2}\)
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\(\frac{7x+2}{5x+7}=\frac{7x-1}{5x+1}=\frac{7x+2-7x+1}{5x+7-5x-1}=\frac{3}{6}=\frac{1}{2}\)
\(2\left(7x+2\right)=5x+7\)
\(14x-5x=7-4\)
\(9x=3\)
\(\Rightarrow x=3\div9\)
\(\Rightarrow x=\frac{1}{3}\)
nhân chéo ta được:
\(\left(7x+2\right)\left(5x+1\right)=\left(5x+7\right)\left(7x-1\right)\)
\(35x^2+7x+10x+2=35x^2-5x+49x-7\) ( nhân phân phối)
\(35x^2-35x^2+7x+10x-5x+49x=-2-7\)
\(-27x=-9\)
\(x=\frac{-9}{-27}\)
\(x=\frac{1}{3}\)
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Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{7x+2}{5x+7}=\frac{7x-1}{5x+1}=\frac{\left(7x+2\right)-\left(7x-1\right)}{\left(5x+7\right)-\left(5x+1\right)}=\frac{3}{6}=\frac{1}{2}\)
=> 2(7x + 2) = 5x + 7
14x + 4 = 5x + 7
14x - 5x = 7 - 4
9x = 3
x = 3:9
x = 0,(3)
\(\frac{37-x}{x+13}=\frac{3}{7}\)
=>7.(37-x)=3.(x+13)
<=>259-7x=3x+39
<=>3x+7x=259-39
<=>10x=220
<=>x=22
\(\frac{37-x}{x+13}=\frac{3}{7}\Leftrightarrow\left(37-x\right).7=\left(x+13\right).3\Leftrightarrow259-7x=3x+39\)(nhân chéo)
\(\Leftrightarrow3x+7x=259-39\Rightarrow10x=220\Rightarrow x=220:10\Rightarrow x=22\)
Vậy x=22