Lời giải:

\(B=\frac{3}{x-1}\sqrt{\frac{(x-1)^2}{(3x)^2}}=\frac{3}{x-1}|\frac{x-1}{3x}|\)

\(=\frac{3}{x-1}.\frac{1-x}{3x}=\frac{-1}{x}\)

\(B=\dfrac{3}{x-1}.\sqrt{\dfrac{x^2-2x+1}{9x^2}}=\dfrac{3}{x-1}.\sqrt{\left(\dfrac{x-1}{3x}\right)^2}\)

\(=\dfrac{3}{x-1}.\left|\dfrac{x-1}{3x}\right|=\dfrac{3}{x-1}.\dfrac{1-x}{3x}=-\dfrac{1}{x}\)

...

a) \(A=\dfrac{1}{x+5}+\dfrac{2}{x-5}-\dfrac{2x+10}{\left(x+5\right)\left(x-5\right)}\)

\(A=\dfrac{x-5+2x+10-2x-10}{\left(x+5\right)\left(x-5\right)}=\dfrac{x-5}{\left(x+5\right)\left(x-5\right)}=\dfrac{1}{x+5}\)

b) \(A=-3\Rightarrow\dfrac{1}{x+5}=-3\)

\(\Leftrightarrow x+5=-\dfrac{1}{3}\Leftrightarrow x=-\dfrac{1}{3}-5=\dfrac{-16}{3}\)

\(9x^2-42x+49=\left(3x-7\right)^2=\left(3.\dfrac{-16}{3}-7\right)^2=\left(-23\right)^2=529\) \(\left(x=\dfrac{-16}{3}\right)\)

A = (x - 1)(x + 3) - (x - 2)(5x - 4)

A = x²  + 2x - 3 - 5x² + 14x - 8

A = -4x² + 16x - 11

B = (3a - 2b)(9a² + 6ab - 4b²)

B = 27a³ + 18a²b - 12ab² - 18a²b - 12ab² + 8b³

B = 27a³ -24ab² + 8b³

C = (x - 1)(x + 1) - (2x - 3)(4 - 5x)

C = x² - 1 - 8x + 10x + 12 - 15x

C = x² - 13x + 11

a, \(9x+3x\left(2x^2+x-3\right)=9x+6x^3+3x^2-9x\)

b, \(\left(3x-1\right)^2-9x\left(x+1\right)=9x^2-6x+1-9x^2-9x=1-15x\)

c, \(\left(x-1\right)^2-x\left(x+1\right)=x^2-2x+1-x^2-x=1-3x\)

(4x - 1)(3 - x) - (2x + 3)(2x - 1) = 0

12x + \(4x^2\)- 3 + x - 4x + 2x - 6x + 3 = 0 

\(4x^2\)+ 5x                                           = 0

4x . 4x + 5x                                           = 0

  16x    + 5x                                           = 0

       21x                                                 = 0

           x                                                 = 0

2x(8x + 3) - (4x - 1)(4x + 1) = 13

16x + 6x   - 16x - 4x + 4x +1 = 13

6x +1                                     = 13

6x                                          = 12

  x                                           = 2

 a, (x + 2) . (x - 2) - (x - 3) . (x + 1).
= x²- 4 -( x² + x -3x -3)
= x^{2 -} 4 -x² -x+ 3x + 3
= 2x-1
b.(2x + 1)² + (3x - 1)² + 2 . (2x + 1) . (3x - 1)
=( 2x +1 + 3x-1)²
=(5x)²
= 25x²

 

Ta có: \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\dfrac{\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{3^{32}-1}{2}\)

Rút gọn: (3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(316 + 1)(3³² + 1)

A=(3-1)(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3²-1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3⁴-1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3⁸-1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3¹⁶-1)(3¹⁶ + 1)(3³² + 1)
A=(3³² - 1)(3³² + 1)
A=3⁶⁴-1
=>A=(3⁶⁴-1) /2