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\(2^3-\left(5x\right)^3-5\times\left(5x\right)^2\)+ 5
\(=8-125x^3-125x^2+5\)
\(=-125x^2\left(x-1\right)+13\)
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a, \(\dfrac{4x+13}{5x\left(x-7\right)}-\dfrac{x-48}{5x\left(7-x\right)}\)
\(=\dfrac{4x+13}{5x\left(x-7\right)}+\dfrac{x-48}{5x\left(x-7\right)}\)
\(=\dfrac{4x+13+x-48}{5x\left(x-7\right)}\)
\(=\dfrac{5x-35}{5x\left(x-7\right)}\)
\(=\dfrac{5\left(x-7\right)}{5x\left(x-7\right)}=\dfrac{1}{x}\)
b, \(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\)
\(=\dfrac{1}{x\left(1-5x\right)}+\dfrac{25x-15}{\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{1+5x}{x\left(x-5x\right)\left(1+5x\right)}+\dfrac{x\left(25x-15\right)}{x\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{1+5x+25x^2-15x}{x\left(1-5x\right)\left(1+5x\right)}\)\(=\dfrac{25x^2-10x+1}{x\left(1-5x\right)\left(1+5x\right)}=\dfrac{\left(5x-1\right)^2}{x.\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{\left(5x-1\right)^2}{-x\left(5x-1\right)\left(1+5x\right)}\) \(=\dfrac{-\left(5x-1\right)}{x\left(1+5x\right)}\)
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(5x-1)(5x+1)=25x2-7x+15
<=> 25x2-1-25x2+7x-15=0
<=>7x=16
=>x=16/7
\(=\left(5x-1\right)^2+\left(5x+1\right)^2-2\left(5x-1\right)\left(5x+1\right)\)
\(=\left(5x-1-5x-1\right)^2\)
\(=\left(-2\right)^2=4\)
(5x-1)2+(5x+1)2-2(25x2-1)=(5x-1)2+(5x+1)2-2(52x2-12)
=(5x-1)2+(5x+1)2-2[(5x2)-12]
=(5x-1)2+(5x+1)2-2(5x-1)(5x+1)
=(5x-1)2+(5x+1)2-(5x-1)(5x+1)-(5x-1)(5x+1)
=(5x-1)(5x-1-5x+1)+(5x+1)(5x+1-5x-1)
=(5x-1).0+(5x+1).0
=0+0
=0