Lời giải:
ĐK: $x\neq 0$
PT $\Rightarrow (400-2x)(x+\frac{1}{4})=400x$
$\Leftrightarrow (200-x)(4x+1)=800x$
$\Leftrightarrow 800x+200-4x^2-x=800x$
$\Leftrightarrow -4x^2-x+200=0$
$\Leftrightarrow 4x^2+x-200=0$
$\Leftrightarrow (2x+\frac{1}{4})^2=\frac{3201}{16}$
$\Rightarrow 2x+\frac{1}{4}=\pm \frac{\sqrt{3201}}{4}$
$\Rightarrow x=-\frac{1}{8}\pm \frac{\sqrt{3201}}{8}$
Bài 1 : Giải pt sau.
\(\left(\frac{400}{x-2}\right)\left(x+\frac{1}{4}\right)=400\)
1) Giải các pt chứa ẩn ở mẫu:
a)\(\frac{x}{2\left(x-3\right)}+\frac{x}{2x+2}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
b) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)
c)\(\frac{1}{x-2}+3=\frac{x-3}{2-x}\)
26 ,giải phương trình.
a,\(\frac{1}{x-1}+\frac{2}{x^2+x+1}=\frac{3x^2}{x^3-1}\)
b,\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
c,\(\frac{x-1}{x+2}+\frac{x-2}{x+1}=\frac{2\left(x^2+2\right)}{x^2-4}\)
d,\(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(x-3\right)}\)
\(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
Giải PT trên.
giải PT sau :\(\frac{3x+2}{x+4}+\frac{2x+1}{x-2}=5-\frac{x-32}{x^2+2x-8}\)
:\(\frac{x+2m}{x+3}+\frac{x-m}{x-3}=\frac{mx\left(x+1\right)}{x^2-9}\)
Giải phương trình sau:
\(\frac{4x^2-\left(x-3\right)^2}{9\left(x^2-1\right)}-\frac{x^2-9}{\left(2x+3\right)^2-x^2}+\frac{\left(2x-3\right)^2-x^2}{4x^2-\left(x+3\right)^2}=1\)
Giải phương trình:
a, \(\frac{2}{\left(1-3x\right)\left(3x+11\right)}=\frac{1}{9x^2-6x+1}-\frac{3}{\left(3x+11\right)^2}\)
b,\(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^1-x+1}=\frac{3}{x\left(x^4+x^2+1\right)}\)
Giải phương trình sau
a) \(\frac{3}{2\left(x+1\right)}-\frac{x-2}{9}=\frac{2x+1}{18}\)
b) \(\frac{2x}{\left(x+1\right)\left(x-2\right)}+\frac{-2}{x-1}=\frac{1}{x+2}\)
1, giải pt sau
a,\(\frac{9}{x}+2=-6\)
b,\(\frac{7}{x+1}+\frac{-18x}{x\left(x^2+4x+3\right)}=\frac{-4}{x+3}\)
c,\(\frac{3x-1}{x-1}-1=\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}\)
