Xét \(x^{27}+x^{24}+x^{21}+x^{18}+x^{15}+x^{12}+x^9+x^6+x^3+1\)

\(=\left(x^{27}+x^{21}+x^{15}+x^9+x^3\right)+\left(x^{24}+x^{18}+x^{12}+x^6+1\right)\)

\(=x^3\left(x^{24}+x^{18}+x^{12}+x^6+1\right)+\left(x^{24}+x^{18}+x^{12}+x^6+1\right)\)

\(=\left(x^3+1\right)\left(x^{24}+x^{18}+x^{12}+x^6+1\right)\)

Vậy ta có

\(VT=\dfrac{x^{24}+x^{18}+x^{12}+x^6+1}{\left(x^3+1\right)\left(x^{24}+x^{18}+x^{12}+x^6+1\right)}=\dfrac{1}{x^3+1}\) (đpcm)

\(\frac{x^{10}-x^8-x^7+x^6+x^6+x^4-x^3-x^2+1}{x^{30}+x^{24}+x^{18}+x^{12}+x^6+1}=\frac{(x^{10}-x^8+x^6)-(x^7-x^5+x^3)+(x^4-x^2+1)}{ (x^{30}+x^{18}+x^{24})+(x^{12}+x^6+1)} \)

=\(\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+x^6+1)(x^{18}+1 )}=\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+2x^6+1-x^6) (x^6+1)(x^{12}-x^6+1)}=\frac{(x^4-x^2+1)(x^6-x^3+1)}{ (x^6-x^3+1)(x^6+x^3+1)(x^2+1)(x^4-x^2+1)(x^12-x^6+1 )} \)

=\(\frac{1}{(x^6+x^2+1)(x^2+1)(x^{12}-x^6+1)}\)

1, 2x - 35 = 15

  2x         =  15 + 35

  2x         =   50

    x         =  50 : 2 

    x         =   25.

2, 3x + 18 = 12

    3x        =  12 - 18

    3x        = -6

     x         =  -6 : 3

     x         =  -2.

3, / x - 1 / = 0

=> x \(\in\varnothing\).

4, -13 /x/ = - 26

  /x/        = -26 : -13

=> \(\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)

 Vậy x \(\in\){ 2 ; -2}.

5,4 - ( 27 - 3 ) = x - ( 13 - 4 )

  4 - 24           = x - 9

  -20               =  x - 9

             -x      =    9 + 20

             -x      =    29

              x      =   -29.

6, 47 - ( x + 15 ) = 21

  47 - x - 15        = 21

       -x - 15         = 21 - 47 

       -x - 15         = -26

             -x          =  -26 + 15 

             -x          =     - 11

              x          = 11.

7, -5 -( 24 - x) = - 11

   -5 - 24 + x   = -11

        -24 + x   = -11 + 5

        -24 + x   =  -6

                 x   = -6 + 24

                 x   =  18.

8, 6 - /x/ = 2

        /x/   = 6 - 2

         \(\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)

Vậy x \(\in\left\{3;-3\right\}.\)

9, 6 + /x/ = 2

         /x/ = 2 - 6

=>      x = -4.

2x - 35 = 15

=> 2x = 15 + 35

=> x = 50 : 2

=> x = 25

3x + 18 = 12

=> 3x = 12 - 18

=> x = ( -6 ) : 3

=> x = -2

| x - 1 | = 0

=> x - 1 = 0

=> x = 0 + 1

=> x = 1

-13 * | x | = -26

=> | x | = -26 : ( -13 )

=> | x | = 2

17 - 2x = -15

2x = 17 - (-15)

2x = 32

x = 32 : 2

x = 16

--------

54 : (x + 2) = -6

x + 2 = 54 : (-6)

x + 2 = -9

x = -9 - 2

x = -11

--------

12.(3 - x) = 72

3 - x = 72 : 12

3 - x = 6

x = 3 - 6

x = -3

-------

-3(x + 5) + 18 = -27

-3(x + 5) = -27 - 18

-3(x + 5) = -45

x + 5 = -45 : (-3)

x + 5 = 15

x = 15 - 5

x = 10

-------

(x + 5)² = 9

x + 5 = 3 hoặc x + 5 = -3

*) x + 5 = 3

x = 3 - 5

x = -2

*) x + 5 = -3

x = -3 - 5

x = -8

Vậy x = -8; x = -2

--------

(3 - x)³ = 27

(3 - x)³ = 3³

3 - x = 3

x = 3 - 3

x = 0

=00

- 3\(x\) + 24  = -24

  3\(x\)          = 24 + 24

   3\(x\)          = 48

     \(x\)           = 48 : 3

     \(x\)           = 16