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a) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{9x^2-6x+1}\)
\(=-\dfrac{9x^2+3x+2x-6x^2}{\left(3x-1\right)\left(3x+1\right)}.\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=-\dfrac{x\left(3x+5\right)}{\left(3x-1\right)^2}.\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{-1}{2}\)
b) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
\(=\left(\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{3x-9-x^2}{3x\left(x+3\right)}\right)\)
\(=\dfrac{x^2-3x+9}{x\left(x-3\right)\left(x+3\right)}.\dfrac{3x\left(x+3\right)}{-x^2+3x-9}\)
\(=\dfrac{x^2-3x+9}{x-3}.\dfrac{3}{-\left(x^2-3x+9\right)}\)
\(=-\dfrac{3}{x-3}\)
a,\(\dfrac{3}{x-3}\) - \(\dfrac{6x}{9-x^2}\) + \(\dfrac{x}{x+3}\) (*)
đkxđ: x khác 3, x khác -3
(*) \(\dfrac{3(x+3)}{\left(x-3\right).\left(x+3\right)}\)- \(\dfrac{6x}{\left(x-3\right).\left(x+3\right)}\) + \(\dfrac{x\left(x+3\right)}{\left(x-3\right).\left(x+3\right)}\)
=>3x+9 -6x + x2+3x
<=>x2 + 3x-6x+3x + 9
<=>x2 +9
<=>(x-3).(x+3)
a: \(=\dfrac{x^4+15x+7}{x^4+15x+7}\cdot\dfrac{x}{14x^2+1}\cdot\dfrac{4x^3+4}{2x^3+2}=\dfrac{2x}{14x^2+1}\)
b: \(=\dfrac{x^7+3x^2+2}{x^7+3x^2+2}\cdot\dfrac{x^2+x+1}{x^3-1}\cdot\dfrac{3x}{x+1}\)
\(=\dfrac{1}{x-1}\cdot\dfrac{3x}{x+1}=\dfrac{3x}{x^2-1}\)
\(ĐKXĐ:1-3x\ne0\Leftrightarrow x\ne\dfrac{1}{3};3x+1\ne0\Leftrightarrow x\ne-\dfrac{1}{3}\)
\(A=\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x}\)
\(A=\left(\dfrac{9x^2+3x+2x-6x^2}{\left(1-3x\right)\left(3x+1\right)}\right):\left(\dfrac{6x^2+10x}{1+3x}\right)\)
\(A=\dfrac{3x^2+5x}{3x+1-9x^2-3x}.\dfrac{1+3x}{6x^2+10}\)
\(A=\dfrac{\left(3x^2+5x\right).\left(1+3x\right)}{\left(1-9x^2\right).2.\left(3x^2+5\right)}\)
\(A=\dfrac{1+3x}{\left(1+3x\right)\left(1-3x\right)}=\dfrac{1}{\left(1-3x\right).2}=\dfrac{1}{2-6x}\)
Hình như đề bị thiếu mũ \(2\) trong \(1-6x+9x\)\(\) đúng không Đinh Diệp
\(A=\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(A=\left(\dfrac{3x\left(1+3x\right)}{\left(1-3x\right)\left(1+3x\right)}+\dfrac{2x\left(1-3x\right)}{\left(1+3x\right)\left(1-3x\right)}\right):\dfrac{2x\left(3x+5\right)}{\left(3x-1\right)^2}\)
\(A=\left[\dfrac{3x\left(1+3x\right)}{\left(1-3x\right)\left(1+3x\right)}+\dfrac{2x\left(1-3x\right)}{\left(1+3x\right)\left(1-3x\right)}\right]:\dfrac{2x\left(3x+5\right)}{\left(3x-1\right)^2}\)
\(A=\left[\dfrac{3x+9x^2}{\left(1-3x\right)\left(1+3x\right)}+\dfrac{2x-6x^2}{\left(1+3x\right)\left(1-3x\right)}\right]:\dfrac{2x\left(3x+5\right)}{\left(3x-1\right)^2}\)
\(A=\left[\dfrac{3x+9x^2+2x-6x^2}{\left(1-3x\right)\left(1+3x\right)}\right].\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(A=\left[\dfrac{3x^2+5x}{-\left(3x-1\right)\left(1+3x\right)}\right].\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(A=\left[\dfrac{x\left(3x+5\right)}{-\left(3x-1\right)\left(1+3x\right)}\right].\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(A=\dfrac{1}{-\left(1+3x\right)}.\dfrac{3x-1}{x}\)
\(A=\dfrac{1}{-1-3x}.\dfrac{3x-1}{x}\)
\(A=\dfrac{3x-1}{-x-3x^2}\)
f: \(=\dfrac{5x-3-x+3}{4x^2y}=\dfrac{4x}{4x^2y}=\dfrac{1}{xy}\)
g: \(=\dfrac{3x+10-x-4}{x+3}=\dfrac{2x+6}{x+3}=2\)
h: \(=\dfrac{4-2+x}{x-1}=\dfrac{x+2}{x-1}\)
n: \(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{x\left(x+3\right)}=\dfrac{2}{x}\)
p: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
k: \(=\dfrac{x-2x-4+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{-6}{x^2-4}\)
m: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
\(M=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{x+5}\)\(\Rightarrow M=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{x+4}{\left(x+4\right)\left(x+5\right)}\)\(\Rightarrow M=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{x+4}\)\(\Rightarrow M=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{x+3}\)
\(\Rightarrow M=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{x+2}\)
\(\Rightarrow M=\dfrac{1}{x+1}\)
M= \(\dfrac{1}{(x+1)(x+2)}\)+ \(\dfrac{1}{(x+2)(x+3)}\)+ \(\dfrac{1}{(x+3)(x+4)}\)+ \(\dfrac{1}{(x+4)(x+5)}\)+ \(\dfrac{1}{x+5}\)
M= \(\dfrac{1}{x+1}\)- \(\dfrac{1}{x+2}\)+ \(\dfrac{1}{x+2}\)- \(\dfrac{1}{x+3}\)+ \(\dfrac{1}{x+3}\)- \(\dfrac{1}{x+4}\)+ \(\dfrac{1}{x+4}\)+ \(\dfrac{1}{x+5}\)
M= \(\dfrac{1}{x+1} + \dfrac{1}{x+5}\)
M= \(\dfrac{x+5}{(x+1)(x+5)} + \dfrac{x+1}{(x+1)(x+5)} \)
M= \(\dfrac{x+5+x+1}{(x+1)(x+5)}\)
M= \(\dfrac{2x+6}{(x+1)(x+5)}\)
M= \(\dfrac{2(x+3)}{(x+1)(x+5)}\)
a: ĐKXĐ: \(x\notin\left\{0;1;2;3;4;5\right\}\)
b: \(P=\dfrac{1}{\left(x-1\right)\cdot x}+\dfrac{1}{\left(x-2\right)\left(x-1\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-4\right)\left(x-5\right)}\)
\(=\dfrac{1}{x-1}-\dfrac{1}{x}+\dfrac{1}{x-2}-\dfrac{1}{x-1}+\dfrac{1}{x-3}-\dfrac{1}{x-2}+\dfrac{1}{x-4}-\dfrac{1}{x-3}+\dfrac{1}{x-5}-\dfrac{1}{x-4}\)
\(=\dfrac{1}{x-5}-\dfrac{1}{x}=\dfrac{x-x+5}{x\left(x-5\right)}=\dfrac{5}{x\left(x-5\right)}\)
a, ĐK : \(x\ne1;2;3;4;5\)
b, \(\dfrac{1}{x\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-4\right)\left(x-5\right)}\)
\(=\dfrac{1}{x}-\dfrac{1}{x-1}+\dfrac{1}{x-1}-\dfrac{1}{x-2}+\dfrac{1}{x-2}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-4}+\dfrac{1}{x-4}-\dfrac{1}{x-5}\)
\(=\dfrac{1}{x}-\dfrac{1}{x-5}=\dfrac{x-5-x}{x\left(x-5\right)}=\dfrac{-5}{x\left(x-5\right)}\)
\(C=\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{1}{4-9x^2}=\dfrac{3x+2-3x+2+1}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{5}{9x^2-4}\)
Hic hic