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Bài 1:
a, \(\frac{1}{x+1}+\frac{2}{x-1}=\frac{1+x^2}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)
\(\Leftrightarrow\) \(\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{1+x^2}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow\) x - 1 + 2(x + 1) = 1 + x2
\(\Leftrightarrow\) x - 1 + 2x + 2 - 1 - x2 = 0
\(\Leftrightarrow\) -x2 + 3x = 0
\(\Leftrightarrow\) x(3 - x) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(TMĐKXĐ\right)\\x=3\left(TMĐKXĐ\right)\end{matrix}\right.\)
Vậy S = {0; 3}
b, \(\frac{x-2}{x+2}-\frac{x}{x-2}=\frac{8}{x^2-4}\) (ĐKXĐ: x \(\ne\) \(\pm\) 2)
\(\Leftrightarrow\) \(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{8}{\left(x+2\right)\left(x-2\right)}\)
\(\Rightarrow\) (x - 2)2 - x(x + 2) = 8
\(\Leftrightarrow\) (x - 2)2 - x(x + 2) - 8 = 0
\(\Leftrightarrow\) x2 - 4x + 4 - x2 - 2x - 8 = 0
\(\Leftrightarrow\) -6x - 4 = 0
\(\Leftrightarrow\) x = \(\frac{-2}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{-2}{3}\)}
c, \(\frac{1}{x}\) + \(\frac{2}{x-3}\) = \(\frac{1-5x}{x^2-3x}\) (ĐKXĐ: x \(\ne\) 0; x \(\ne\) 3)
\(\Leftrightarrow\) \(\frac{x-3}{x\left(x-3\right)}+\frac{2x}{x\left(x-3\right)}=\frac{1-5x}{x\left(x-3\right)}\)
\(\Rightarrow\) x - 3 + 2x = 1 - 5x
\(\Leftrightarrow\) 3x - 3 = 1 - 5x
\(\Leftrightarrow\) 3x + 5x = 1 + 3
\(\Leftrightarrow\) 8x = 4
\(\Leftrightarrow\) x = \(\frac{1}{2}\) (TMĐKXĐ)
Vậy S = {\(\frac{1}{2}\)}
Bài 2:
a, \(\frac{1}{x+2}=\frac{5}{2-x}+\frac{12+x}{x^2-4}\)
\(\Leftrightarrow\) \(\frac{1}{x+2}=\frac{-5}{x-2}+\frac{12+x}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\) \(\frac{x-2}{\left(x+2\right)\left(x-2\right)}=\frac{-5\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{12+x}{\left(x+2\right)\left(x-2\right)}\)
\(\Rightarrow\) x - 2 = -5(x + 2) + 12 + x
\(\Leftrightarrow\) x - 2 = -5x - 10 + 12 + x
\(\Leftrightarrow\) x - 2 = -4x + 2
\(\Leftrightarrow\) x + 4x = 2 + 2
\(\Leftrightarrow\) 5x = 4
\(\Leftrightarrow\) x = \(\frac{4}{5}\)
Vậy S = {\(\frac{4}{5}\)}
Chúc bn học tốt!! (Phần b hình như không có gì thì phải)
\(\Leftrightarrow\frac{5\left(x+5\right)-3\left(x-3\right)}{15}=\frac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Leftrightarrow\frac{2x+34}{15}=\frac{2x+34}{x^2+2x-15}\Leftrightarrow\orbr{\begin{cases}2x+34=0\\x^2+2x-15=15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-17\\x^2+2x-30=0\end{cases}}\)
Từ đó tìm được \(S=\left\{-17;\sqrt{31}-1;-\sqrt{31}-1\right\}\)
\(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
\(< =>\frac{\left(x-3\right).4}{20}-\frac{\left(2x-1\right).2}{20}=\frac{\left(x+1\right).10}{20}+\frac{5}{20}\)
\(< =>4x-12-4x+2=10x+10+5\)
\(< =>10x=-10-10-5=-25\)
\(< =>x=-\frac{25}{10}=-\frac{5}{2}\)
\(\frac{x+3}{2}-\frac{2x-1}{3}-1=\frac{x+5}{5}\)
\(< =>\frac{\left(x+3\right).15}{30}-\frac{\left(2x-1\right).10}{30}-\frac{30}{30}=\frac{\left(x+5\right).5}{30}\)\(< =>15x+45-20x+10-30=5x+25\)
\(< =>-5x+25=5x+25< =>10x=0< =>x=0\)
1, Đk x≠2;-2
\(\frac{x+2}{2x-4}-\frac{4x}{x^2-4}=0\\ =>\frac{x+2}{2\left(x-2\right)}-\frac{4x}{\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{\left(x+2\right)^2}{2\left(x^2-4\right)}-\frac{8x}{2\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{x^2+4x+4-8x}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x^2-4x+4}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x-2}{2\left(x+2\right)}=0\\ =>x-2=0\\ =>x=2\left(loại\right)\)
a)\(2+\frac{3}{x-5}=1\)
\(\Rightarrow\frac{3}{x-5}=-1\)
\(\Rightarrow3=-x+5\)
\(\Leftrightarrow x+3=5\)
\(\Rightarrow x=2\)
Bài 1:
1, \(\frac{2x-5}{x+5}=3\) (ĐKXĐ: x \(\ne\) -5)
\(\Leftrightarrow\) \(\frac{2x-5}{x+5}=\frac{3\left(x+5\right)}{x+5}\)
\(\Rightarrow\) 2x - 5 = 3(x + 5)
\(\Leftrightarrow\) 2x - 5 = 3x + 15
\(\Leftrightarrow\) 2x - 3x = 15 + 5
\(\Leftrightarrow\) -x = 20
\(\Leftrightarrow\) x = -20 (TMĐKXĐ)
Vậy S = {-20}
2, \(\frac{4}{x+1}=\frac{3}{x-2}\) (ĐKXĐ: x \(\ne\) -1; x \(\ne\) 2)
\(\Leftrightarrow\) \(\frac{4\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}=\frac{3\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}\)
\(\Rightarrow\) 4(x - 2) = 3(x + 1)
\(\Leftrightarrow\) 4x - 8 = 3x + 3
\(\Leftrightarrow\) 4x - 3x = 3 + 8
\(\Leftrightarrow\) x = 11 (TMĐKXĐ)
Vậy S = {11}
3, \(\frac{5}{2x-3}=\frac{1}{x-4}\) (ĐKXĐ: x \(\ne\) \(\frac{3}{2}\); x \(\ne\) 4)
\(\Leftrightarrow\) \(\frac{5\left(x-4\right)}{\left(2x-3\right)\left(x-4\right)}=\frac{2x-3}{\left(2x-3\right)\left(x-4\right)}\)
\(\Rightarrow\) 5(x - 4) = 2x - 3
\(\Leftrightarrow\) 5x - 20 = 2x - 3
\(\Leftrightarrow\) 5x - 2x = -3 + 20
\(\Leftrightarrow\) 3x = 17
\(\Leftrightarrow\) x = \(\frac{17}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{17}{3}\)}
Bài 2:
1, \(\frac{1}{x-1}+\frac{2}{x+1}=\frac{5x-3}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)
\(\Leftrightarrow\) \(\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{5x-3}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow\) x + 1 + 2(x - 1) = 5x - 3
\(\Leftrightarrow\) x + 1 + 2x - 2 = 5x - 3
\(\Leftrightarrow\) 3x - 1 = 5x - 3
\(\Leftrightarrow\) 3x - 5x = -3 + 1
\(\Leftrightarrow\) -2x = -2
\(\Leftrightarrow\) x = 1 (KTM)
\(\Rightarrow\) Pt vô nghiệm
Vậy S = \(\varnothing\)
2, \(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\) (ĐKXĐ: x \(\ne\) 2; x \(\ne\) 0)
\(\Leftrightarrow\) \(\frac{x\left(x+2\right)}{x\left(x-2\right)}-\frac{x-2}{x\left(x-2\right)}=\frac{2}{x\left(x-2\right)}\)
\(\Rightarrow\) x(x + 2) - x + 2 = 2
\(\Leftrightarrow\) x2 + 2x - x + 2 = 2
\(\Leftrightarrow\) x2 + x = 2 - 2
\(\Leftrightarrow\) x2 + x = 0
\(\Leftrightarrow\) x(x + 1) = 0
\(\Leftrightarrow\) x = 0 hoặc x + 1 = 0
\(\Leftrightarrow\) x = 0 và x = -1
Ta có: x = 0 KTM đkxđ
\(\Rightarrow\) x = -1
Vậy S = {-1}
3, \(\frac{5}{x-3}-\frac{3}{x+3}=\frac{3x}{x^2-9}\) (ĐKXĐ: x \(\ne\) \(\pm\) 3)
\(\Leftrightarrow\) \(\frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{3x}{\left(x-3\right)\left(x+3\right)}\)
\(\Rightarrow\) 5(x + 3) - 3(x - 3) = 3x
\(\Leftrightarrow\) 5x + 15 - 3x + 9 = 3x
\(\Leftrightarrow\) 2x + 24 = 3x
\(\Leftrightarrow\) 2x - 3x = 24
\(\Leftrightarrow\) -x = 24
\(\Leftrightarrow\) x = -24 (TMĐKXĐ)
Vậy S = {-24}
Chúc bn học tốt!!
Mình tính mãi vẫn có chỗ sai, mong bạn thông cảm!!
Mình bt mình sai đâu r Garuda
câu 3 bài 3 cuối có cái đoạn 2x + 24 = 3x
\(\Leftrightarrow\) 2x - 3x = -24 (đoạn kia mình ghi là 24 nên quên không đổi dấu)
\(\Leftrightarrow\) -x = -24
\(\Leftrightarrow\) x = 24
Vậy S = {24}
(mình sửa lại rồi nha, chắc hết chỗ sai rồi)