\(\dfrac{4}{2x-3}+\dfrac{4x}{4x^2-9}=\dfrac{1}{2x+3}\) đkxđ x\(\ne\dfrac{3}{2};\dfrac{-3}{2}\)
\(\Leftrightarrow\dfrac{4\left(2x+3\right)}{4x^2-9}+\dfrac{4x}{4x^2-9}=\dfrac{2x-3}{4x^2-9}\)
\(\Leftrightarrow8x+12+4x=2x-3\)
<=>8x+4x-2x=-3-12
<=>10x=-15
=>x=\(\dfrac{-3}{2}\)(loại vì không thuộc đkxđ)
=>\(S\in\varnothing\)
\(a,\dfrac{1}{x^2+3x+2}-\dfrac{3}{x^2-x-2}=\dfrac{-1}{x^2-4}\)
\(b,\dfrac{2x-1}{x^2+4x-5}+\dfrac{x-2}{x^2-10x+9}=\dfrac{3x-12}{x^2-4x-45}\)
b \(\dfrac{4}{2x-3}+\dfrac{4x}{4x^2-1}=\dfrac{7}{2x-1}\)
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) \(\dfrac{4x^{2} + 10}{x^{2} + 5} - \dfrac{9}{x^{2} + 4} = \dfrac{8}{x^{2} + 3} + \dfrac{6}{x^{2} + 1}\)
1) \(\dfrac{4x+7}{x-1}\) = \(\dfrac{12x+5}{3x+4}\)
2) \(\dfrac{x}{x-1}\) - \(\dfrac{2x}{x^{2^{ }}-1}\) = 0
3) \(\dfrac{1}{3-x}\) - \(\dfrac{14}{x^2-9}\) = 1
4) \(\dfrac{x+1}{x-1}\) - \(\dfrac{x-1}{x+1}\) = \(\dfrac{4}{x^2-1}\)
5) x + \(\dfrac{1}{x}\) = x2 + \(\dfrac{1}{x^2}\)
6) \(\dfrac{x-1}{x^2+4}\) = \(\dfrac{x-1}{x+1}\)
giải phương trình:
\(\dfrac{4x}{x^2+4x+3}\)-1 = 6 \(\left(\dfrac{1}{x+3}-\dfrac{1}{2x+2}\right)\)
a) \(\dfrac{4x-8}{2x+1}\)=0 b) 2-\(\dfrac{x}{x-2}\)=\(\dfrac{x+1}{x+2}\) c)\(\dfrac{x+2}{x-3}\)=\(\dfrac{x}{x+1}\) d) \(\dfrac{3}{x-2}\)=\(\dfrac{1}{x}\) e) \(\dfrac{x-2}{x}\)=\(\dfrac{x-3}{x+2}\) f) \(\dfrac{2x}{x+1}\)-\(\dfrac{1}{x-2}\)=\(\dfrac{2x^2-16}{\left(x+1\right)\left(x-2\right)}\) g) \(\dfrac{3x}{x-1}+\dfrac{2}{x+1}=\dfrac{3x^2}{\left(x-1\right)\left(x+1\right)}\) h) \(\dfrac{1-x}{4}=\dfrac{2x+1}{5}\) i)\(\dfrac{2-3x}{3}=\dfrac{x+4}{4}\) m) \(\dfrac{4x+3}{5}=\dfrac{3-4x}{3}\) n) \(\dfrac{7-3x}{4}-2=\dfrac{x+5}{3}\)
Giải các phương trình sau :
a) \(\dfrac{1-6x}{x-2}+\dfrac{9x+4}{x+2}=\dfrac{x\left(3x-2+1\right)}{x^2-4}\)
b) \(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\)
c) \(\dfrac{2}{x-1}+\dfrac{2x+3}{x^2+x+1}=\dfrac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)
d) \(\dfrac{x^3-\left(x-1\right)^3}{\left(4x+3\right)\left(x-5\right)}=\dfrac{7x-1}{4x+3}-\dfrac{x}{x-5}\)
Giải phương trình:
a) \(\dfrac{5}{x^2+x-6}\) - \(\dfrac{2}{x^2+4x+3}\) = \(\dfrac{-3}{2x-1}\)
b) \(\dfrac{4x^2+16}{x^2+6}\) = \(\dfrac{3}{x^2+1}\) + \(\dfrac{5}{x^2+3}\)+ \(\dfrac{7}{x^2+5}\)
\(\dfrac{2x-1}{1+2x+4x^2}+\dfrac{2}{2x-1}=\dfrac{8x+2}{1-8x^3}\)
