Tìm x nha m.n
\(\frac{2x}{3}\)= \(\frac{5}{7}\)
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7 tháng 2 2018
ĐKXĐ : \(\hept{\begin{cases}x^2+x-6\ne0\\x^2+4x+3\ne0\\2x-1\ne0\end{cases}\Leftrightarrow\hept{\begin{cases}\left(x+3\right)\left(x-2\right)\ne0\\\left(x+1\right)\left(x+3\right)\ne0\\x\ne\frac{1}{2}\end{cases}\Rightarrow\hept{\begin{cases}x\ne2;-3\\x\ne-1;-3\\x\ne\frac{1}{2}\end{cases}}}}\)
TXĐ : \(x\ne\left\{-3;-1;\frac{1}{2};2\right\}\)
\(pt\Leftrightarrow\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{2}{\left(x+1\right)\left(x+3\right)}=\frac{-3}{2x-1}\)
\(\Leftrightarrow\frac{5\left(x+1\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+3\right)}=\frac{-3}{2x-1}\)
\(\Leftrightarrow\frac{3x+9}{\left(x-2\right)\left(x+1\right)\left(x+3\right)}=\frac{-3}{2x-1}\)
\(\Leftrightarrow\frac{3}{\left(x-2\right)\left(x+1\right)}=\frac{-3}{2x-1}\)
\(\Leftrightarrow\frac{1}{x^2-x-2}=\frac{1}{1-2x}\)
\(\Leftrightarrow x^2-x-2-1+2x=0\)
\(\Leftrightarrow x^2+x-3=0\)
\(\Leftrightarrow\left(x^2+2.\frac{1}{2}.x+\frac{1}{4}\right)-\frac{13}{4}=0\)
\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2-\left(\frac{\sqrt{13}}{2}\right)^2=0\)
\(\Leftrightarrow\left(x+\frac{1-\sqrt{13}}{2}\right)\left(x+\frac{1+\sqrt{13}}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{\sqrt{13}-1}{2}\\x=\frac{-\sqrt{13}-1}{2}\end{cases}}\)
BT
7 tháng 2 2018
\(\frac{5}{x^2+x-6}-\frac{2}{x^2+4+3}=-\frac{3}{2x-1}\)
<=> \(\frac{5}{\left(x-2\right)\left(x+3\right)}-\frac{2}{\left(x+1\right)\left(x+3\right)}=-\frac{3}{2x-1}\)
<=> \(\frac{5\left(x+1\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}=-\frac{3}{2x-1}\)
<=> \(\frac{5x+5-2x+4}{\left(x-2\right)\left(x+3\right)}=-\frac{3}{2x-1}\)
<=> \(\frac{3x+9}{\left(x-2\right)\left(x+3\right)}=-\frac{3}{2x-1}\)
<=> \(\frac{3\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=-\frac{3}{2x-1}\)
<=> \(\frac{1}{x-2}=-\frac{1}{2x-1}\)
<=> x-2=1-2x <=> 3x=3
=> x=1
Đáp số: x=1
HP
7 tháng 5 2016
\(\frac{7^{x+2}+7^{x+1}+7^x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
<=>\(\frac{7^x\left(7^2+7+1\right)}{57}=\frac{5^{2x}.\left(1+5+5^3\right)}{131}\)
<=>\(\frac{7^x.57}{57}=\frac{5^{2x}.131}{131}\)
<=>\(7^x=5^{2x}\)<=>\(7^x=10^x\)<=>x=0
Vậy x=0
LD
7 tháng 2 2018
\(\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4}\)
Đặt a = x2 - 2x + 3. Khi đó phương trình trở thành:
\(\frac{1}{a+1}+\frac{2}{a}=\frac{6}{a-1}\) \(ĐK:\)\(\hept{\begin{cases}a\ne0\\a\ne1\\a\ne-1\end{cases}}\)
\(\Leftrightarrow\)\(\frac{a\left(a-1\right)}{a\left(a-1\right)\left(a+1\right)}+\frac{2\left(a-1\right)\left(a+1\right)}{a\left(a-1\right)\left(a+1\right)}=\frac{6a\left(a+1\right)}{a\left(a-1\right)\left(a+1\right)}\)
\(\Rightarrow\)\(a^2-a+2a^2-2-6a^2-6a=0\)
\(\Leftrightarrow\)\(-3a^2-7a-2=0\)
\(\Leftrightarrow\)\(\left(a-6\right)\left(a-1\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}a-6=0\\a-1=0\end{cases}}\)
\(\Rightarrow\)\(\orbr{\begin{cases}x^2-2x-3=0\\x^2-2x+2=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-3\\x=1\end{cases}\left(x^2-2x+2\ne0\right)}\)
Vậy \(S=\left\{-3;1\right\}\)
2 tháng 7 2019
\(a,\frac{7}{x+2}=\frac{3}{x-5}\)
\(\Rightarrow7\left(x-5\right)=3\left(x+2\right)\)
\(\Rightarrow7x-35=3x+6\)
\(\Rightarrow7x-3x=6+35\)
\(\Rightarrow4x=41\)
\(\Rightarrow x=\frac{41}{4}\)
\(b,\frac{2x+5}{2x}-\frac{x}{x+5}=0\)
\(\Rightarrow\frac{2x+5}{2x}=\frac{x}{x+5}\)
\(\Rightarrow\left(2x+5\right)\left(x+5\right)=2x\cdot x\)
\(\Rightarrow2x^2+10x+5x+25=2x^2\)
\(\Rightarrow2x^2+15x+25-2x^2=0\)
\(\Rightarrow15x+25=0\)
\(\Rightarrow15x=-25\)
\(\Rightarrow x=\frac{-5}{3}\)
\(c,\frac{12x+1}{11x-4}+\frac{10x-4}{9}=\frac{20x+17}{18}\)
\(\Rightarrow\frac{12x+1}{11x-4}=\frac{20x+17}{18}-\frac{10x-4}{9}\)
\(\Rightarrow\frac{12x+1}{11x-4}=\frac{25}{18}\)
\(\Rightarrow\left(12x+1\right)\cdot18=25\cdot\left(11x-4\right)\)
\(\Rightarrow216x+18=275x-100\)
\(\Rightarrow216x-275x=-100-18\)
\(\Rightarrow-59x=-118\)
\(\Rightarrow x=2\)
3 tháng 5 2019
1 ) (2/3 - 1/2) . x = 5/12
(4/6 - 3/6) . x = 5/12
1/6 . x = 5/12
x = 5/12 : 1/6
x = 5/2
2 ) TH1 :
x + 1/2 = 0
x = 0 - 1/2
x = -1/2
TH2 :
2/3 - 2x = 0
2x = 2/3 - 0
2x = 2/3
x = 2/3 : 2
x = 1/3
F
1
S
5 tháng 10 2017
\(\Leftrightarrow\frac{7^x.7+7^x.7^2+7^x}{57}=\frac{5^{2x}.1+5^{2x}.5+5^{2x}.5^3}{131}\)
\(\Leftrightarrow\frac{7^x\left(7+49+1\right)}{57}=\frac{5^{2x}\left(1+5+125\right)}{131}\)
\(\Leftrightarrow\frac{7^x.57}{57}=\frac{5^{2x}.131}{131}\)
<=> 7x = 52x
<=> \(\frac{7^x}{5^{2x}}=1\)
<=> \(\frac{7^x}{25^x}=1\)
<=> \(\left(\frac{7}{25}\right)^x=1\)
<=> x = 0
3 tháng 12 2017
a, (x-15):5+22=24
( x - 15 ) : 5 = 2
x-15 = 10
x = 25
15/14 nha bạn
\(\frac{2x}{3}=\frac{5}{7}\)
=> \(2x.7=5.3\)
=> \(2x.7=15\)
=> \(2x=\frac{15}{7}\)
=> \(x=\frac{15}{7}:2\)
=> \(x=\frac{15}{7}.\frac{1}{2}\)
=> \(x=\frac{15}{14}\)