Nhân chéo vào là ra
chuyển vế phức tạp thành vế đơn gian rồi giải hệ pt ra là xong
Lời giải:
ĐKXĐ: $x\neq -2; -3; -4;-5;-6$
PT \(\Leftrightarrow \frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}=\frac{1}{8}\)
\(\Leftrightarrow \frac{1}{x+2}-\frac{1}{x+6}=\frac{1}{8}\)
\(\Leftrightarrow (x+2)(x+6)=32\)
\(\Leftrightarrow x^2+8x-20=0\Leftrightarrow (x-2)(x+10)=0\Rightarrow x=2\) hoặc $x=-10$
Giải các phương trình sau:
1. \(a,\dfrac{6}{x-1}-\dfrac{4}{x-3}=\dfrac{8}{2x-6}\)
\(b,\dfrac{1}{x-2}+\dfrac{5}{x+1}=\dfrac{3}{2-x}\)
\(c,\dfrac{3x}{x-2}-\dfrac{x}{x-5}=\dfrac{3x}{\left(x-2\right)\left(5-x\right)}\)
2. \(a,\left(x+2\right)\left(3-4x\right)=x^2+4x+4\)
\(b,2x^2-6x+1\)
Giải phương trình sau:
\(\dfrac{x-1}{2013}\)+\(\dfrac{x-2}{2012}\)+\(\dfrac{x-3}{2011}\)=\(\dfrac{x-4}{2010}\)+\(\dfrac{x-5}{2009}\)+\(\dfrac{x-6}{2008}\)
Giải phương trình sau: \(1+\dfrac{x-2}{1-x}+\dfrac{2x^2-5}{x^3-1}=\dfrac{4}{x^2+x+1}\)
4.Giải phương trình
a) \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)
b)\(\dfrac{1}{x-1}+\dfrac{2}{x+1}=\dfrac{x}{x^2-1}\)
c)\(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)
d)\(\dfrac{90}{x}-\dfrac{36}{x-6}=2\)
e)\(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\)
f)\(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)
g)\(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\)
h)\(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)
i)\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
k)\(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\)
l)\(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)
m)\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
Cần gấp ạ
Giải phương trình :
\(\dfrac{x}{10}+\dfrac{x-1}{9}+\dfrac{x-2}{8}+\dfrac{x-3}{7}+\dfrac{x-4}{6}+\dfrac{x-5}{5}\)= 6
Giải phương trình sau :
a, \(\dfrac{x+3}{x+2}-\dfrac{x+4}{x+3}=\dfrac{x+5}{x+4}-\dfrac{x+6}{x+5}\)
b, \(\dfrac{x+1}{x-2}-\dfrac{12}{x^2-4}=\dfrac{x+7}{x+2}\)
Giải phương trình:
b) \(\dfrac{7}{2}-\left(\dfrac{x}{5}-\dfrac{1}{4}\right)=\dfrac{9}{2}\)
c) (x+2) . (x-5). (x-6) (x+3) = 180
d) \(x-\dfrac{\dfrac{x}{2}-\dfrac{3+x}{4}}{2}=\dfrac{2x-\dfrac{10-7x}{3}}{2}-x-1\)
e) \(\left(\dfrac{1}{1.101}+\dfrac{1}{2.102}+........+\dfrac{1}{10.110}\right).\left(x-3\right)=\dfrac{1}{1.11}+\dfrac{1}{2.12}+.......+\dfrac{1}{100.110}\)
Giải các phương trình sau:
a) \(\dfrac{x+1}{35}+\dfrac{x+3}{33}=\dfrac{x+5}{31}+\dfrac{x+7}{29}\)
b) \(\dfrac{x-10}{1994}+\dfrac{x-8}{1996}+\dfrac{x-6}{1998}+\dfrac{x-4}{2000}+\dfrac{x-2}{2002}=\dfrac{x-2002}{2}+\dfrac{x-2000}{4}+\dfrac{x-1998}{6}+\dfrac{x-1996}{8}+\dfrac{x-1994}{10}\)
Bài 1: Giải phương trình
\(a,\dfrac{x+1}{2009}+\dfrac{x+3}{2007}=\dfrac{x+5}{2005}+\dfrac{x+7}{1993}\)
\(b,\left(x+2\right)^4+\left(x+4\right)^4=14\)
\(c,\left(x-3\right)\left(x-2\right)x+1=60\)
d, \(2x^4+3x^3-x^2+3x+2=0\)
