Ta có: \(\dfrac{6}{x-5}+\dfrac{2}{x-8}=\dfrac{18}{\left(x-5\right)\left(8-x\right)}-1\)
\(\Leftrightarrow6x-48+2x-10=-18-\left(x-5\right)\left(x-8\right)\)
\(\Leftrightarrow8x-58+18+x^2-13x+40=0\)
\(\Leftrightarrow x^2-5x=0\)
\(\Leftrightarrow x\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(nhận\right)\\x=5\left(loại\right)\end{matrix}\right.\)
Giải các bất phương trình sau :
a) \(4x-8\ge3\left(3x-1\right)-2x+1\)
b) \(\left(x-3\right)\left(x+2\right)+\left(x+4\right)^2\le2x\left(x+5\right)+4\)
c) \(3x-\dfrac{x+2}{3}\le\dfrac{3\left(x-2\right)}{2}+5-x\)
d) \(x-\dfrac{x+2}{3}\ge3x-1+\dfrac{x}{2}\)
e) \(\dfrac{x\left(x+2\right)}{3}+\dfrac{\left(x-1\right)\left(x+2\right)}{2}\ge\dfrac{5\left(x+1\right)^2}{6}+1\)
f) \(\dfrac{x+5}{2012}+\dfrac{x+6}{2011}+\dfrac{x+7}{2010}>-3\)
a \(x^2-x=0\) b \(x^2-2x=0\) c (x+1)(x+2)=(2-x)(x+2)
d \(\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\) đ \(\dfrac{8-x}{x-7}-8=\dfrac{1}{x-7}\)
e \(\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x+1\right)}=\dfrac{2x}{\left(x+1\right)\left(x-3\right)}\)
f \(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)
g \(\dfrac{90}{x}-\dfrac{36}{x-6}=2\) h \(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\) i \(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)
k \(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\) l \(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)
m\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
n \(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\) j \(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)
q \(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
Cần gấp ạ
a) tính A =\(\dfrac{-45.58-45.42}{2+4+6+.......+16+18}\)
b) tìm x biết 1-(\(\left(5\dfrac{3}{8}+x-7\dfrac{5}{24}\right):\left(-16\dfrac{2}{3}\right)=0\)
\(gpt\\ 8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+4\right)^2\)
Bài 1:Giải các pt chứa ẩn ở mẫu sau:
a) \(\dfrac{2x+1}{x-1}=\dfrac{5\left(x-1\right)}{x+1}\) b) \(\dfrac{x+3}{x+1}+\dfrac{x-2}{x}=2\) c)\(\dfrac{x-2}{2+x}-\dfrac{3}{x-2}=\dfrac{2\left(x-11\right)}{x^2-4}\)
d)\(\dfrac{x+1}{x-2}-\dfrac{x-1}{x+2}=\dfrac{2\left(x^2+2\right)}{x^2-4}\) e)\(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{4}{x^2-1}\) g)\(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{5x-2}{4-x^2}\)
h)\(\dfrac{1}{x+1}-\dfrac{5}{x-2}=\dfrac{15}{\left(x+1\right)\left(2-x\right)}\) j)\(\dfrac{3}{4\left(x-5\right)}+\dfrac{15}{50-2x^2}=\dfrac{7}{6\left(x+5\right)}\) k)\(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
n)\(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\)
Bài 1: GPT
a) \(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}=\dfrac{4x^2}{x^2-4}\)
b) \(\dfrac{6}{x-1}-\dfrac{4}{x-3}=\dfrac{8}{\left(x-1\right)\left(x-3\right)}\)
c)\(\dfrac{x+3}{x-3}-\dfrac{48}{x^2-9}=\dfrac{x-3}{x+3}\)
Bài 1: Giải các phương trình và bất phương trình sau:
a. \(\dfrac{1}{x+2}-\dfrac{2}{x-1}=\dfrac{4x-8}{\left(x+2\right)\left(x-1\right)}\)
b. \(2x-3\ge5\)
c. \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{2x-6}{\left(x+1\right)\left(x-2\right)}\)
d. \(3x-5\ge7\)
Rút gọn:
\(A=\dfrac{x}{5-x}+\left(\dfrac{x}{x^2-25}+\dfrac{5-x}{5x+x^2}\right):\dfrac{2x-5}{x^2+5x}\)
\(B=\left[\left(\dfrac{1}{x^2}+1\right)\cdot\dfrac{1}{1+2x+x^2}+\left(1+\dfrac{1}{x}\right)\cdot\dfrac{2}{\left(1+x\right)^3}\right]:\dfrac{x-1}{x^3}\)
rút gọn các biểu thức sau
\(B=\dfrac{3\text{x}^2+6\text{x}+12}{x^3-8\dfrac{ }{ }}\)
C=\(\left(\dfrac{x+1}{2\text{x}-2}+\dfrac{3}{x^2-1}-\dfrac{x+3}{2\text{x}+2}\right).\dfrac{4\text{x}^2-4}{5}\)
E=\(\dfrac{x^2-10\text{x}+25}{x^2-5\text{x}}\)
