(x-1)2 = 9/4
(x-1)2= 25/9
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27 tháng 2 2021
1) ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
Ta có: \(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{4}{x^2-1}\)
\(\Leftrightarrow\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{\left(x-1\right)\left(x+1\right)}\)
Suy ra: \(x^2+2x+1-\left(x^2-2x+1\right)=4\)
\(\Leftrightarrow x^2+2x+1-x^2+2x-1=4\)
\(\Leftrightarrow4x=4\)
hay x=1(loại)
Vậy: \(S=\varnothing\)
2) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
Ta có: \(\dfrac{x+2}{x-2}+\dfrac{x}{x+2}=2\)
\(\Leftrightarrow\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2\left(x^2-4\right)}{\left(x-2\right)\left(x+2\right)}\)
Suy ra: \(x^2+4x+4+x^2-2x=2x^2-8\)
\(\Leftrightarrow2x^2+2x+4-2x^2-8=0\)
\(\Leftrightarrow2x-4=0\)
\(\Leftrightarrow2x=4\)
hay x=2(loại)
Vậy: \(S=\varnothing\)
LP
2
8 tháng 12 2017
125(28+72)-25(3^2.4+64)
=125.100-25(9.4+64)
=125.100-25.(36+64)
=125.100-25.100
=12500-2500
=10000
10 tháng 5 2022
1: \(\left(3x-\dfrac{1}{5}\right)^2=\left(-\dfrac{3}{25}\right)^2\)
=>3x-1/5=3/25 hoặc 3x-1/5=-3/25
=>3x=8/25 hoặc 3x=2/25
=>x=8/75 hoặc x=2/75
2: \(\left(2x-\dfrac{1}{3}\right)^2=\left(-\dfrac{2}{9}\right)^2\)
=>2x-1/3=2/9 hoặc 2x-1/3=-2/9
=>2x=5/9 hoặc 2x=1/9
=>x=5/18 hoặc x=1/18
10 tháng 7 2023
1: =-2/9(15/17+2/17)=-2/9
2: \(=\dfrac{-6}{3}+\dfrac{-21}{90}\)
=-2-7/30=-67/30
3: \(=\dfrac{3}{4}\cdot\dfrac{7}{5}+\dfrac{9}{7}\cdot\dfrac{3}{2}\)
=21/20+27/14=417/140
4: =-25/13(5/19+14/19)=-25/13
5: =-7/5-45/21=-7/5-15/7=-124/35
10 tháng 7 2023
1: =-2/9(15/17+2/17)=-2/9
2: =−63+−2190=−63+−2190
=-2-7/30=-67/30
3: =34⋅75+97⋅32=34⋅75+97⋅32
=21/20+27/14=417/140
4: =-25/13(5/19+14/19)=-25/13
5: =-7/5-45/21=-7/5-15/7=-124/35
22 tháng 7 2017
a)
\(3:\left(\dfrac{9}{4}\right)=\dfrac{3}{4}:\left(6.x\right)\\ \Rightarrow3.6.x=\dfrac{3}{4}.\dfrac{9}{4}\\ x=\dfrac{3}{4}.\dfrac{9}{4}.\dfrac{1}{3}.\dfrac{1}{6}\\ x=\dfrac{3}{4.4.2}\\ x=\dfrac{3}{32}\)
b)
\(4,5:0,3=\left(5.0,09\right):\left(0,01.x\right)\\ 0,01.x.4,5=5.0,09.0,3\\ x=5.\dfrac{9}{100}.\dfrac{3}{10}.100.\dfrac{10}{45}\\ x=3\)
d)
\(\left(\dfrac{1}{9}.x\right)=\dfrac{7}{4}:\dfrac{2}{25}\\ \left(\dfrac{1}{9}.x\right)=\dfrac{7}{4}.\dfrac{25}{2}\\ x:\dfrac{7}{4}=\dfrac{25}{2}:\dfrac{1}{9}\\ x=\dfrac{25}{2}.9.\dfrac{7}{4}\\ x=\dfrac{1575}{8}\\ x=196\dfrac{7}{8}\)
e)
\(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\\ -x.x=-2.\dfrac{8}{25}\\ -x^2=-\dfrac{16}{25}=-\dfrac{4^2}{5^2}\\ -x^2=-\left(\dfrac{4}{5}\right)^2\\ \Rightarrow x=\dfrac{4}{5}\)
Chúc bạn học tốt 
+) <=>\(\orbr{\begin{cases}x-1=\frac{3}{2}\\x-1=\frac{-3}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=-\frac{1}{2}\end{cases}}}\)
+) <=>\(\orbr{\begin{cases}x-1=\frac{5}{3}\\x-1=-\frac{5}{3}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{8}{3}\\x=-\frac{2}{3}\end{cases}}}\)