\(\Leftrightarrow\dfrac{x^2+2x+1-1}{x+1}+\dfrac{x^2+8x+16+4}{x+4}=\dfrac{x^2+4x+4+2}{x+2}+\dfrac{x^2+6x+9+3}{x+3}\)
\(\Leftrightarrow x+1-\dfrac{1}{x+1}+x+4+\dfrac{4}{x+4}=x+2+\dfrac{2}{x+2}+x+3+\dfrac{3}{x+3}\)
\(\Leftrightarrow2x+5-\dfrac{1}{x+1}+\dfrac{4}{x+4}=2x+5+\dfrac{2}{x+2}+\dfrac{3}{x+3}\)
=>-x-4+4x+4=2x+6+3x+6
=>3x=5x+12
=>-2x=12
hay x=-6(nhận)
23) \(\dfrac{1}{x^2+4x+3}+\dfrac{1}{x^2+8x+15}+\dfrac{1}{x^2+12x+35}=\dfrac{1}{9}\)
24) \(\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}+\dfrac{1}{x^2+11x+30}=\dfrac{1}{8}\)
25) \(\dfrac{x^2+2x+2}{x+1}+\dfrac{x^2+8x+20}{x+4}=\dfrac{x^2+4x+6}{x+2}+\dfrac{x^2+6x+12}{x+3}\)
Giải phương trình
\(1,\dfrac{x^2-2x-3}{x-1}+\dfrac{x^2-8x+20}{x-4}=\dfrac{x^2-4x+6}{x-2}+\dfrac{x^2-6x+12}{x-3}\)
\(2,\left(1+\dfrac{1}{1\cdot3}\right)\cdot\left(1+\dfrac{1}{2\cdot4}\right)\cdot\left(1+\dfrac{1}{3\cdot5}\right)\cdot...\cdot[1+\dfrac{1}{x\cdot\left(x+2\right)}]=\dfrac{31}{16}\left(x\in N\right)\)
Giải Pt \(\dfrac{14}{20-6x-2x^2}+\dfrac{x^2+4x}{x^2+5x}-\dfrac{x+3}{2-x}+3=0\)
Giải pt:
a) \(\dfrac{x+1}{x^2+2x+4}-\dfrac{x-2}{x^2-2x+4}=\dfrac{6}{x(x^4+4x^2+16)}\)
b) \(\dfrac{4x^{2} + 10}{x^{2} + 5} - \dfrac{9}{x^{2} + 4} = \dfrac{8}{x^{2} + 3} + \dfrac{6}{x^{2} + 1}\)
Giải các PT sau:
1) \(\dfrac{1}{x^2+4x+3}+\dfrac{1}{x^2+8x+15}+\dfrac{1}{x^2+12x+35}=\dfrac{1}{9}\)
2) \(\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}+\dfrac{1}{x^2+11x+30}=\dfrac{1}{15}\)
Giúp mình với!!!
Giúp mk nha
Giải các phương trình
1/ \(\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}=\dfrac{1}{6}\)
2/ \(\dfrac{1}{x^2-6x+8}+\dfrac{1}{x^2-10x+24}+\dfrac{1}{x^2-14x+48}=\dfrac{1}{9}\)
3/ \(\dfrac{1}{x^2-3x+3}+\dfrac{2}{x^2-3x+4}=\dfrac{6}{x^2-3x+5}\)
4/ \(\dfrac{6}{\left(x+1\right)\left(x+2\right)}+\dfrac{8}{\left(x-1\right)\left(x+4\right)}=1\)
5/ \(4\left(x^3+\dfrac{1}{x^3}\right)=13\left(x+\dfrac{1}{x}\right)\)
6/ \(\dfrac{4x}{4x^2-8x+7}+\dfrac{3x}{4x^2-10x+7}=1\)
7/ \(\dfrac{x^2-3x+5}{x^2-4x+5}-\dfrac{x^2-5x+5}{x^2-6x+5}=-\dfrac{1}{4}\)
8/ \(x.\dfrac{8-x}{x-1}\left(x-\dfrac{8-x}{x-1}\right)=15\)
5.c) \(\dfrac{x+1}{x^2+x+1}-\dfrac{x-1}{x^2-x-1}=\dfrac{3}{x\left(x^4+x^2+1\right)}\)
6.b) \(\dfrac{4}{2x^3+3x^2-8x-12}-\dfrac{1}{x^2-4}-\dfrac{4}{2x^2+7x+6}+\dfrac{1}{2x+3}=0\)
B1 : Giải phương trình
a. \(\dfrac{x-2}{x-4}-\dfrac{1}{x-2}=-2\)
b. \(\dfrac{x-2}{x+3}-\dfrac{x+1}{3-x}=\dfrac{2x^2+6}{x^2-9}\)
c. \(\dfrac{2x-1}{3}-\dfrac{x-6}{4}=\dfrac{3x-2}{2}\)
d. \(\dfrac{3x-1}{4}+\dfrac{8x-21}{20}=\dfrac{3\left(x+2\right)}{5}-2\)
Giải pt :
\(\dfrac{x+2}{x^2+2x+4}+\dfrac{x-2}{x^2-2x+4}=\dfrac{6}{x\left(x^4+4x^2+16\right)}\)
