Lời giải:
ĐKXĐ: $x\neq -1; x\neq 3$
PT \(\Leftrightarrow \frac{x}{2(x+1)}-\frac{2x}{(x+1)(x-3)}-\frac{x}{2(3-x)}=0\)
\(\Leftrightarrow \frac{x}{2(x+1)}-\frac{2x}{(x+1)(x-3)}+\frac{x}{2(x-3)}=0\)
\(\Leftrightarrow \frac{x(x-3)}{2(x+1)(x-3)}-\frac{4x}{2(x+1)(x-3)}+\frac{x(x+1)}{2(x-3)(x+1)}=0\)
\(\Rightarrow x(x-3)-4x+x(x+1)=0\)
\(\Leftrightarrow 2x^2-6x=0\)
\(\Leftrightarrow 2x(x-3)=0\Rightarrow x=0\) hoặc $x=3$
Kết hợp với ĐKXĐ suy ra $x=0$
\(1.\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4}
\)
2.\(\frac{2x^4}{\left(x+1\right)^2}-\frac{5x^2}{x+1}+2=0\)
3.\(\left(x+\frac{1}{x}\right)^2-6\left(x+\frac{1}{x}\right)+8=0\)
4.\(\left(x^2+\frac{1}{x^2}\right)-4\left(x+\frac{1}{x}\right)+6=0\)
5.\(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)
GIÚP MÌNH VỚI!!
a) \(\frac{x}{2x-6}+\frac{x}{2x+2}+\frac{2x}{\left(x+1\right)\left(3-x\right)}=0\)
b) \(\frac{x-3}{x+1}-\frac{x+1}{x+3}=\frac{x^2-x-10}{x^2+4x+3}\)
\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
Giải các pt chứa ẩn ở mẫu:
a) \(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\)
b) \(\frac{2x-5}{x+5}=3\)
c) \(\frac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}=0\)
a.\(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{16}{x^2-1}\)
b.\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0\)
c.\(\frac{12}{8-x^3}=1+\frac{1}{x+2}\)
d.\(\frac{x+25}{2x^2-50}-\frac{x+5}{x^2-5x}=\frac{5-x}{2x^2+10x}\)
e.\(\frac{4}{x^2+2x-3}=\frac{2x-5}{x+3}-\frac{2x}{x-1}\)
Giari các phương trình sau.
a. \(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)
b. \(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\)
c. \(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\)
d. \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\)
e. \(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
f. \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\)
g. \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{3}{2}\)
h. \(\frac{x-1}{x}-\frac{1}{x+1}=\frac{2x-1}{x^2+x}\)
giải phương trình
a) \(\frac{4x-17}{2x^2+5}=0\)
b) \(\frac{\left(x^2-2x\right)-\left(3x+6\right)}{x+2}=0\)
c) \(\frac{x^2-x-6}{x-3}=0\)
d) \(\frac{2x-5}{x+5}=3\)
e) \(\frac{5}{3x+2}=2x-1\)
Đề bài: Giải phương trình :
a) \(\frac{x}{2x+2}-\frac{2x}{x^2-2x-3}=\frac{x}{6-2x}\)
b) \(\frac{5}{-x^2+5x-6}+\frac{x+3}{2-x}=0\)
c) \(\frac{3}{x^2+x-2}-\frac{1}{x-1}=\frac{-4}{x+2}\)
Các cậu giúp tớ với, càng chi tiết càng tốt ạ. Tớ cảm ơn trước nhé !
2) \(\frac{x-3}{5}=6-\frac{1-2x}{3}\)
3) \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)
4)\(\frac{2x+3}{3}=\frac{5-4x}{2}\)
5.\(\frac{5x+3}{12}=\frac{1+2x}{9}\)
