e tách ra nhé.☘

;))

Bài 2:

\(\dfrac{a+b}{a-b}=\dfrac{c+a}{c-a}\)

\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a-b}{c-a}=\dfrac{a+b+a-b}{c+a+c-a}=\dfrac{a}{c}\) (T/c dãy tỷ số = nhau)

\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a}{c}\Rightarrow c\left(a+b\right)=a\left(c+a\right)\)

\(\Rightarrow ac+bc=ac+a^2\Rightarrow a^2=bc\)

c) \(5x-7=3x+9\)

d) \(5x-\left|9-7x\right|=3\)

e) \(-5+\left|3x-1\right|+6=\left|-4\right|\)

h) \(5^{-1}.25^x=125\)

\(\Rightarrow\frac{1}{5}.25^x=125\)

\(\Rightarrow25^x=125:\frac{1}{5}\)

\(\Rightarrow25^x=625\)

\(\Rightarrow25^x=25^2\)

\(\Rightarrow x=2\)

Vậy \(x=2.\)

Chúc bạn học tốt!

g) \(\left(x-1\right)^2=\left(x-1\right)^4\)

\(\Rightarrow\left(x-1\right)^2-\left(x-1\right)^4=0\)

\(\Rightarrow\left(x-1\right)^2.\left[1-\left(x-1\right)^2\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^2=0\\1-\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0+1\\x-1=1\\x-1=-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=1+1\\x=\left(-1\right)+1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)

Vậy \(x\in\left\{1;2;0\right\}.\)

i) \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|=4x\)

Ta có:

\(\left\{{}\begin{matrix}\left|x+1\right|\ge0\\\left|x+2\right|\ge0\\\left|x+3\right|\ge0\end{matrix}\right.\forall x.\)

\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+3\right|\ge0\) \(\forall x.\)

\(\Rightarrow4x\ge0\)

\(\Rightarrow x\ge0.\)

Lúc này ta có: \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)=4x\)

\(\Rightarrow x+1+x+2+x+3=4x\)

\(\Rightarrow\left(x+x+x\right)+\left(1+2+3\right)=4x\)

\(\Rightarrow3x+6=4x\)

\(\Rightarrow6=4x-3x\)

\(\Rightarrow6=1x\)

\(\Rightarrow x=6\left(TM\right).\)

Vậy \(x=6.\)

Chúc bạn học tốt!

a) 1/4(x-3)+2=1/5

1/4.(x-3) = 1/5-2

1/4.(x-3) = -9/5

x-3 = (-9/5):1/4

x-3 = -36/5

x = -36/5+3

x= -21/5

a.-1,75-(-\(\dfrac{1}{9}\)-2\(\dfrac{1}{8}\))
-1,75-\(\dfrac{1}{9}+\dfrac{17}{8}\)
\(-\dfrac{7}{4}-\dfrac{1}{9}+\dfrac{17}{8}\)
\(\dfrac{-126}{72}-\dfrac{8}{72}+\dfrac{153}{72}\)
=\(\dfrac{19}{72}\)

b.\(\dfrac{-1}{12}-\left(2\dfrac{5}{8}-\dfrac{1}{3}\right)\)
\(\dfrac{-1}{12}-\left(\dfrac{21}{8}-\dfrac{1}{3}\right)\)
\(\dfrac{-1}{12}-\dfrac{21}{8}+\dfrac{1}{3}\)
\(\dfrac{-2}{24}-\dfrac{63}{24}+\dfrac{64}{24}\)
=\(\dfrac{-1}{24}\)