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Nhiều vậy ai làm hết được :P
1) \(\frac{3x-2}{3}-2=\frac{4x+1}{4}\)
\(\Leftrightarrow\frac{3x-8}{3}=\frac{4x-1}{4}\)
\(\Leftrightarrow4\left(3x-8\right)=3\left(4x-1\right)\)
\(\Leftrightarrow12x-32=12x-3\)(vô lí)
Vậy pt vô nghiệm
P/s: mấy câu sau tương tự thôi mà :)))
nhăm nhe 1 câu thôi
\(10,\frac{3+5x}{5}-3=\frac{9x-3}{4}\)
\(\Leftrightarrow\frac{3+5x-15}{5}=\frac{9x-3}{4}\)
\(\Leftrightarrow\frac{-12+5x}{5}=\frac{9x-3}{4}\)
\(\Leftrightarrow\left(-12+5x\right)5=\left(9x-3\right)4\)
\(\Leftrightarrow-60+25x=36x-12\)
\(\Leftrightarrow26x-36x=-12+60\)
\(\Leftrightarrow-10x=48\)
\(\Leftrightarrow x=-4,8\)
a) \(\left(x+8\right)\left(x+6\right)=104+x^2\Leftrightarrow x^2+6x+8x+48=104+x^2\)
\(\Leftrightarrow x^2+6x+8x-x^2=104-48\Leftrightarrow14x=56\Leftrightarrow x=\dfrac{56}{14}=4\)
vậy \(x=4\)
b) \(\left(x+1\right)\left(x+2\right)-\left(x-3\right)\left(x+4\right)=6\)
\(\Leftrightarrow x^2+2x+x+2-\left(x^2+4x-3x-12\right)=6\)
\(\Leftrightarrow x^2+2x+x+2-x^2-4x+3x+12=6\)
\(\Leftrightarrow2x+14=6\Leftrightarrow2x=6-14=-8\Leftrightarrow x=\dfrac{-8}{2}=-4\)
vậy \(x=-4\)
c) \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(\Leftrightarrow4x^2-20x-\left(4x^2-3x-4x+3\right)=5\)
\(\Leftrightarrow4x^2-20x-4x^2+3x+4x-3=5\)
\(\Leftrightarrow-13x-3=5\Leftrightarrow-13x=5+3=8\Leftrightarrow x=\dfrac{8}{-13}=\dfrac{-8}{13}\)
vậy \(x=\dfrac{-8}{13}\)
d) \(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)
\(\Leftrightarrow3x^2-6x-4x+8=3x^2-27x-3\)
\(\Leftrightarrow3x^2-6x-4x-3x^2+27x=-3-8\)
\(\Leftrightarrow17x=-11\Leftrightarrow x=\dfrac{-11}{17}\) vậy \(x=\dfrac{-11}{17}\)
e) câu này đề bị thiếu rồi nha bn
f) \(5x\left(x-3\right)=\left(x-2\right)\left(5x-1\right)-5\)
\(\Leftrightarrow5x^2-15x=5x^2-x-10x+2-5\)
\(\Leftrightarrow5x^2-15x-5x^2+x+10x=2-5\)
\(\Leftrightarrow-4x=-3\Leftrightarrow x=\dfrac{-3}{-4}=\dfrac{3}{4}\) vậy \(x=\dfrac{3}{4}\)
a) \(\left(x+8\right)\left(x+6\right)=104+x^2\)
\(\Leftrightarrow x^2+14x+48=104+x^2\)
\(\Leftrightarrow14x=56\)
\(\Rightarrow x=4\)
b) \(\left(x+1\right)\left(x+2\right)-\left(x-3\right)\left(x+4\right)=6\)
\(\Leftrightarrow x^2+3x+2-x^2-7x+12=6\)
\(\Leftrightarrow-4x=-8\)
\(\Rightarrow x=2\)
c) \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(\Leftrightarrow4x^2-20x-4x^2+3x+4x-3=5\)
\(\Leftrightarrow-13x=8\)
\(\Rightarrow x=\dfrac{-8}{13}\)
d) \(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)
\(\Leftrightarrow3x^2-10x+8=3x^2-27x-3\)
\(\Leftrightarrow17x=-11\)
\(\Rightarrow x=\dfrac{-11}{17}\)
e) \(\left(x-5\right)\left(x-4\right)-\left(x+1\right)\left(x-2\right)=7\)
\(\Leftrightarrow x^2-9x+20-x^2+x+2=7\)
\(\Leftrightarrow-8x=-15\)
\(\Rightarrow x=\dfrac{15}{8}\)
f) \(5x\left(x-3\right)=\left(x-2\right)\left(5x-1\right)-5\)
\(\Leftrightarrow5x^2-15x=5x^2-11x+2-5\)
\(\Leftrightarrow-4x=-3\)
\(\Rightarrow x=\dfrac{3}{4}\)
1/ \(1+\frac{2}{x-1}+\frac{1}{x+3}=\frac{x^2+2x-7}{x^2+2x-3}\)
ĐKXĐ: \(\hept{\begin{cases}x-1\ne0\\x+3\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne1\\x\ne-3\end{cases}}\)
<=> \(1+\frac{2\left(x+3\right)+x-1}{\left(x-1\right)\left(x+3\right)}=\frac{x^2+2x-3-5}{x^2+2x-3}\)
<=> \(1+\frac{2x+6+x-1}{x^2+2x-3}=1-\frac{5}{x^2+2x-3}\)
<=> \(\frac{3x+5}{x^2+2x-3}+\frac{5}{x^2+2x-3}=1-1\)
<=> \(\frac{3x+5}{x^2+2x-3}+\frac{5}{x^2+2x-3}=0\)
<=> \(\frac{3x+10}{x^2+2x-3}=0\)
<=> \(3x+10=0\)
<=> \(x=-\frac{10}{3}\)
bài 1:
a) (x+1)^2-(x-1)^2-3(x+1)(x-1)
=(x+1+x-1)(x+1-x+1)-3x^2-3
=2x^2-3x^2-3
=-x^2-3
1) (x+1)2+2x=x(x+1)+6
⇔x2+2x+1+2x=x2+x+6
⇔x2+2x+1+2x-x2-x-6=0
⇔3x-5=0
⇔x=\(\frac{5}{3}\)
Vậy tập nghiệm của phương trình đã cho là:S={\(\frac{5}{3}\)}
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+...+\dfrac{1}{\left(x+6\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+8\right)}\)
\(=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+...+\dfrac{1}{x+7}-\dfrac{1}{x+8}\)
\(=\dfrac{1}{x}-\dfrac{1}{x+8}=\dfrac{8}{x\left(x+8\right)}\)