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ĐK: x#0; x#-1
\(\frac{x^4}{1-x}\)+ x3 + x2 + 1
= \(\frac{x^4}{1-x}\)+ \(\frac{x^3\left(1-x\right)}{1-x}\)+ \(\frac{x^2\left(1-x\right)}{1-x}\)+ \(\frac{1-x}{1-x}\)
= \(\frac{x^4+x^3-x^4+x^2-x^3+1-x}{1-x}\)
= \(\frac{x+1}{1-x}\)
a: \(\Leftrightarrow x\left(16-x^2\right)+x^3-125=3\)
=>16x-125=3
=>16x=128
hay x=8
b: \(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-10\)
\(\Leftrightarrow6x^2+2-6x^2+12x-6=-10\)
=>12x-4=-10
=>12x=-6
hay x=-1/2
c: \(\Leftrightarrow x^3-27+x\left(4-x^2\right)=1\)
\(\Leftrightarrow4x-27=1\)
hay x=7
a: \(=\dfrac{5x+30}{x\left(x-3\right)\left(x+2\right)}+\dfrac{4x+12}{x\left(x+2\right)}-\dfrac{x}{x-3}\)
\(=\dfrac{5x+30+4\left(x^2-9\right)-x^2\left(x+2\right)}{x\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{5x+30+4x^2-36-x^3-2x^2}{x\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{-x^3+2x^2+5x-6}{x\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{-x^3-2x^2+4x^2+8x-3x-6}{x\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{\left(x+2\right)\left(-x^2+4x-3\right)}{x\left(x+2\right)\left(x-3\right)}=\dfrac{-\left(x-1\right)}{x}\)
b: \(=\dfrac{x}{x+1}-\dfrac{1}{\left(x-1\right)\left(x+1\right)}+\dfrac{x^5+x+1}{\left(x+1\right)\left(x^3-1\right)}\)
\(=\dfrac{x^2-x-1}{\left(x+1\right)\left(x-1\right)}+\dfrac{x^3-x^2+1}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2-x-1+x^3-x^2+1}{\left(x+1\right)\left(x-1\right)}=\dfrac{x^3-x}{\left(x+1\right)\left(x-1\right)}=x\)
a: \(=\dfrac{4}{x+2}-\dfrac{3}{x-2}+\dfrac{12}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{4x-8-3x-6+12}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\)
b: \(=\dfrac{6x+3\left(x-1\right)+2\left(x-2\right)}{6}=\dfrac{6x+3x-3+2x-4}{6}=\dfrac{11x-7}{6}\)
c: \(=\dfrac{1}{3x-2}-\dfrac{4}{3x+2}+\dfrac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\dfrac{3x+2-12x+8+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{-6x+4}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{-2}{3x+2}\)
a, \(\dfrac{x^2-x}{x-2}+\dfrac{4-3x}{x-2}\)
\(=\dfrac{x^2-x+4-3x}{x-2}=\dfrac{x^2-4x+4}{x-2}\)
c) \(\dfrac{2}{x^2-9}+\dfrac{1}{x+3}\)
Ta có: \(\dfrac{1}{x+3}=\dfrac{1\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\dfrac{x-3}{x^2-9}\)
\(\Rightarrow\dfrac{2}{x^2-9}+\dfrac{1}{x+3}=\dfrac{2}{x^2-9}+\dfrac{x-3}{x^2-9}=\dfrac{2+x-3}{x^2-9}=\dfrac{x-1}{x^2-9}\)
Chọn đáp án D