\(\dfrac{4}{x-5}-\dfrac{1}{x+5}+\dfrac{13x-x^2}{25-x^2}=\dfrac{4x+20-x+5}{x^2-25}+\dfrac{x^2-13x}{x^2-25}\)
\(=\dfrac{3x+25+x^2-13x}{x^2-25}=\dfrac{x^2-10x+25}{\left(x-5\right)\left(x+5\right)}=\dfrac{\left(x-5\right)^2}{\left(x-5\right)\left(x+5\right)}=\dfrac{x-5}{x+5}\)
Tìm x:
\(\dfrac{x-5}{100}+\dfrac{x-4}{100}+\dfrac{x-3}{100}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
\(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=-5\)
\(\dfrac{2-x}{2001}-1=\dfrac{1-x}{2002}-\dfrac{x}{2003}\)
Bài 1:cho phương trình
a,\(\left(x-1\right)^3-x\left(x-1\right)^2=5x\left(2-x\right)-11\left(x+2\right)\)
b,\(\dfrac{\left(x+10\right)\left(x+4\right)}{12}-\dfrac{\left(x+4\right)\left(2-x\right)}{4}=\dfrac{\left(x+10\right)\left(x-2\right)}{3}\)
c,\(\dfrac{2\left(x-3\right)}{7}+\dfrac{x-5}{3}=\dfrac{13x+4}{21}\)
d,\(\dfrac{2x-1}{5}-\dfrac{x-2}{3}=\dfrac{x+7}{5}\)
e,\(\left(x-2\right)^3+\left(3x-1\right)\left(3x+1\right)=\left(x+1\right)^3\)
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
thực hiên phép tính
a.\(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
b.\(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
Giải PT sau: \(\dfrac{1}{x^2+9x+20}+\dfrac{1}{x^2+11x+30}+\dfrac{1}{x^2+13x+42}=\dfrac{1}{18}\)
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. \(a,\left(x+2\right)\left(3-4x\right)=x^2+4x+4\)
\(b,2x^2-6x+1\)
Tính
\(\dfrac{1}{x^2+7x+10}+\dfrac{1}{x^2+13x+40}+\dfrac{1}{x^2+19x+88}+\dfrac{1}{x^2+25x+154}\)
tìm x,y viết dưới dạng phân số
a. \(5+\dfrac{x}{5+\dfrac{2}{5+\dfrac{3}{5+\dfrac{4}{5}}}}=\dfrac{x}{1+\dfrac{5}{2+\dfrac{4}{3+\dfrac{3}{5+\dfrac{1}{6}}}}}\)
b.
\(\dfrac{y}{3+\dfrac{5}{2+\dfrac{4}{2+\dfrac{5}{2+\dfrac{4}{2+\dfrac{5}{3}}}}}}+\dfrac{y}{7+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{4}}}}\)
= 2
c,
\(x.\left(\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+1}}}}}}}}\right)=\)\(2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}}}}\)+\(x.\left(3+\dfrac{1}{3-\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3-\dfrac{1}{3}}}}}\right)\)
Giair bằng máy tính casio
Giải phương trình :
a)\(\dfrac{3x-2}{5}+\dfrac{x-1}{9}=\dfrac{14x-3}{15}-\dfrac{2x+1}{9}\)
b)\(\dfrac{x+3}{2}-\dfrac{2-x}{3}-1=\dfrac{x+5}{6}\)
c)\(\dfrac{x+5}{2010}+\dfrac{x+4}{2011}+\dfrac{x+3}{2012}+\dfrac{x+2}{2013}=-4\)
d)\(\dfrac{x-12}{77}+\dfrac{x-11}{78}=\dfrac{x-74}{15}+\dfrac{x-72}{16}\)