\(\frac{2x+2}{3x-6}=\frac{2x-6}{3x-15}\)
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HT
2
18 tháng 12 2016
Ta có:\(\frac{2x+2}{3x-6}=\frac{2x-6}{3x-15}\)
\(\Rightarrow\frac{2\left(x+1\right)}{3\left(x-2\right)}=\frac{2\left(x-3\right)}{3\left(x-5\right)}\)
\(\Rightarrow\frac{2}{3}\cdot\frac{x+1}{x-2}=\frac{2}{3}\cdot\frac{x-3}{x-5}\)
\(\Rightarrow\frac{x+1}{x-2}=\frac{x-3}{x-5}\)
\(\Rightarrow\frac{x+1}{x-2}-1=\frac{x-3}{x-5}-1\)
\(\Rightarrow\frac{x+1-x+2}{x-2}=\frac{x-3-x+5}{x-5}\)
\(\Rightarrow\frac{3}{x-2}=\frac{2}{x-5}\)
\(\Rightarrow3\left(x-5\right)=2\left(x-2\right)\)
\(\Rightarrow3x-15=2x-4\)
\(\Rightarrow3x-2x=-4+15\)
\(\Rightarrow x=11\)
NM
1
18 tháng 11 2016
\(\frac{2x+2}{3x-6}=\frac{2x-6}{3x-15}\)
\(\Rightarrow\left(2x+2\right)\left(3x-15\right)=\left(2x-6\right)\left(3x-6\right)\)
\(\Rightarrow6x^2-30x+6x-30=6x^2-12x-18x+36\)
\(\Rightarrow6x^2-30x+6x-6x^2+12x+18x=36+30\)
\(\Rightarrow6x=66\)
\(\Rightarrow x=11\)
k mk nha
HN
16 tháng 12 2018
\(a,\frac{2x+4}{10}+\frac{2-x}{15}=\frac{\left(2x+4\right).3}{10.3}+\frac{\left(2-x\right).2}{15.2}\)
\(=\frac{6x+12}{30}+\frac{4-2x}{30}=\frac{6x+12+4-2x}{30}=\frac{4x+16}{30}\)
\(=\frac{4.\left(x+4\right)}{30}=\frac{2\left(x+4\right)}{15}\)
\(b,\frac{3x}{10}+\frac{2x-1}{15}+\frac{2-x}{20}=\frac{3x.6}{10.6}+\frac{\left(2x-1\right).4}{15.4}+\frac{\left(2-x\right).3}{20.3}\)
\(=\frac{18x}{60}+\frac{8x-4}{60}+\frac{6-3x}{60}=\frac{18x+8x-4+6-3x}{60}=\frac{23x+2}{60}\)
\(c,\frac{x+1}{2x-2}+\frac{x^2+3}{2-2x^2}=\frac{x+1}{2\left(x-1\right)}+\frac{x^2+3}{2\left(1-x^2\right)}=\frac{x+1}{2\left(x-1\right)}+\frac{-x^2-3}{2\left(x^2-1\right)}\)
\(=\frac{x+1}{2\left(x-1\right)}+\frac{-x^2-3}{2\left(x-1\right)\left(x+1\right)}\)\(=\frac{\left(x+1\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}+\frac{-x^2-3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}=\frac{2x-2}{2\left(x-1\right)\left(x+1\right)}=\frac{2\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\)\(=\frac{1}{x+1}\)
DV
20 tháng 12 2016
a. \(=\frac{x+1}{2.\left(x+3\right)}+\frac{2x+3}{x.\left(x+3\right)}=\frac{x^2+x+4x+6}{2x.\left(x+3\right)}=\frac{x^2+5x+6}{2x.\left(x+3\right)}=\frac{\left(x+2\right).\left(x+3\right)}{2x.\left(x+3\right)}=\frac{x+2}{2x}\)
b. =\(\frac{2.\left(x+3\right)}{x.\left(3x-1\right)}.\frac{-\left(3x-1\right)}{x.\left(x+3\right)}=\frac{-2}{x^2}\)
Chắc chắn đúng, mik nhaaaaaa
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 10 2019
a/ ĐKXĐ: ...
\(\Leftrightarrow2\left(x^2-5x-6\right)+\sqrt{x^2-5x-6}-3=0\)
Đặt \(\sqrt{x^2-5x-6}=a\ge0\)
\(2a^2+a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x^2-5x-6}=1\Leftrightarrow x^2-5x-7=0\)
b/ ĐKXĐ: ...
\(\Leftrightarrow5\sqrt{3x^2-4x-2}-2\left(3x^2-4x-2\right)+3=0\)
Đặt \(\sqrt{3x^2-4x-2}=a\ge0\)
\(-2a^2+5a+3=0\) \(\Rightarrow\left[{}\begin{matrix}a=3\\a=-\frac{1}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{3x^2-4x-2}=3\Leftrightarrow3x^2-4x-11=0\)
c/ \(\Leftrightarrow x^2+2x-6+\sqrt{2x^2+4x+3}=0\)
Đặt \(\sqrt{2x^2+4x+3}=a>0\Rightarrow x^2+2x=\frac{a^2-3}{2}\)
\(\frac{a^2-3}{2}-6+a=0\Leftrightarrow a^2+2a-15=0\Rightarrow\left[{}\begin{matrix}x=3\\x=-5\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{2x^2+4x+3}=3\Leftrightarrow2x^2+4x-6=0\)
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 10 2019
d/ ĐKXĐ: ...
Đặt \(\sqrt{\frac{3x-1}{x}}=a>0\)
\(2a=\frac{1}{a^2}+1\Leftrightarrow2a^3-a^2-1=0\)
\(\Leftrightarrow\left(a-1\right)\left(2a^2+a+1\right)=0\)
\(\Rightarrow a=1\Rightarrow\sqrt{\frac{3x-1}{x}}=1\Leftrightarrow3x-1=x\)
e/ĐKXĐ: ...
\(\Leftrightarrow2\sqrt{\frac{6x-1}{x}}=\frac{x}{6x-1}+1\)
Đặt \(\sqrt{\frac{6x-1}{x}}=a>0\)
\(2a=\frac{1}{a^2}+1\Leftrightarrow2a^3-a^2-1=0\Leftrightarrow\left(a-1\right)\left(2a^2+a+1\right)=0\)
\(\Rightarrow a=1\Rightarrow\sqrt{\frac{6x-1}{x}}=1\Rightarrow6x-1=x\)
f/ ĐKXĐ: ...
Đặt \(\sqrt{\frac{x}{2x-1}}=a>0\)
\(\frac{1}{a}+1+a=3a^2\)
\(\Leftrightarrow3a^3-a^2-a-1=0\)
\(\Leftrightarrow\left(a-1\right)\left(3a^2+2a+1\right)=0\)
\(\Leftrightarrow a=1\Rightarrow\sqrt{\frac{x}{2x-1}}=1\Rightarrow x=2x-1\)
27 tháng 5 2016
\(A=\left(\frac{1+2x}{2.\left(2+x\right)}-\frac{x}{3.\left(x-2\right)}+\frac{2x^2}{3.\left(4-x^2\right)}\right).\frac{24-12x}{6+13x}\)
\(=\left[\frac{3.\left(1+2x\right)\left(2-x\right)-2x\left(x+2\right)+4x^2}{2.3.\left(x+2\right)\left(2-x\right)}\right].\frac{24-12x}{6+13x}\)
\(=\frac{6+9x-6x^2-2x^2-4x+4x^2}{6.\left(4-x^2\right)}.\frac{24-12x}{6+13x}\)
\(=\frac{6+5x-4x^2}{6.\left(4-x^2\right)}.\frac{12.\left(2-x\right)}{6+13x}\) \(=\frac{\left(6+5x-4x^2\right).2}{\left(x+2\right)\left(6+13x\right)}=\frac{12+10x-8x^2}{13x^2+32x+12}\)
=> (2x+2)(3x-15) = (3x-6)(2x-6)
=> 6x2-30x+6x-30 = 6x2-18x-12x+36
=> 6x2-30x+6x-30-6x2+18x+12x-36 = 0
=> 6x - 96 = 0
=> 6x = 96
=> x = 96/6
=> x = 16
Vậy x = 16