\(C=\dfrac{\sqrt{\dfrac{4x^2+4x+1}{x}}}{\sqrt{x}\cdot\left|2x^2-x-1\right|}=\dfrac{\left|2x+1\right|}{\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}\cdot\left|\left(x-1\right)\left(2x+1\right)\right|}\)

\(=\dfrac{1}{x\left|x-1\right|}\)

\(A=\left(4x+5\right)^2-\left(3x-7\right)^2-\left(4x-1\right)\left(4x+1\right)\)

\(=\left(4x\right)^2+2.4x.5+5^2-\left[\left(3x\right)^2-2.3x.7+7^2\right]-\left[\left(4x\right)^2-1^2\right]\)

\(=16x^2+40x+25-\left(9x^2-42x+49\right)-\left(16x^2-1\right)\)

\(=16x^2+40x+25-9x^2+42x-49-16x^2+1=-9x^2+82x-23\)

A=(4x+5)²-(3x-7)²-(4x-1)(4x+1)

=16x²+40x+25-9x²+42x-49-16x²+1

=(16x²-9x²-16x²)+(40x+42x)+(25-49+1)

=-9x²+82x-23

\(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\left(ĐK:0\le x\ne\frac{1}{4}\right)\)

\(=\frac{\sqrt{x}-4x+4x-1}{1-4x}:\frac{\left(1+2x\right)+2\sqrt{x}\left(1+2\sqrt{x}\right)+4x-1}{1-4x}\)

\(=\frac{\sqrt{x}-1}{1-4x}.\frac{1-4x}{10x+2\sqrt{x}}=\frac{\sqrt{x}-1}{2\sqrt{x}\left(5\sqrt{x}+1\right)}\)

N=2(2x + 5 )^2 - 3(1 + 4x )(1 - 4x)

= 2 (4x^2 + 20x + 25) - 3(1 - 16x^2)

= 8x^2 + 40x + 50 - 3 + 48x^2

= 56x^2 + 40x - 47

(.....????!!!!!!.....)

\(=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}:\frac{2\left(x+1\right)^2}{4\left(x-1\right)^2}=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}.\frac{4\left(x-1\right)^2}{2\left(x+1\right)^2}=2\)

( 4x-1)³+(4x-3)(16x²+3)

=64x³-48x²+12x-1+64x³+12x-48x²-9

=128x³-96x²+24x-10