a, 117 - \(x\) = 28 - (-7)

   117 - \(x\) = 28 + 7

    117 - \(x\) = 35

            \(x\) =  117 - 35

             \(x\) = 82

b, \(x\) - (-38 - 2\(x\)) = (-3) - 8 + 2\(x\) 

    \(x\) + 38 + 2\(x\) = - 11 + 2\(x\)

   3\(x\)  + 38       = - 11 + 2\(x\)

   3\(x\) - 2\(x\)        = - 11 - 38

   \(x\)                = - 49

d: \(\dfrac{x^4-2x^3+2x-1}{x^2-1}\)

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

\(=x^2-2x+1\)

\(=\left(x-1\right)^2\)

c: =>\(\dfrac{2x-1}{\left(x+5\right)\left(x-1\right)}+\dfrac{x-2}{\left(x-1\right)\left(x-9\right)}=\dfrac{3x-12}{\left(x-9\right)\left(x+5\right)}\)

=>(2x-1)(x-9)+(x-2)(x+5)=(3x-12)(x-1)

=>2x^2-19x+9+x^2+3x-10=3x^2-15x+12

=>-16x-1=-15x+12

=>-x=13

=>x=-13

a: =>x+38+2x=-3-8+2x

=>3x+38=2x-11

=>x=-49

b: \(\Leftrightarrow65+x-15-5x=12-5x\)

=>-4x+50=-5x+12

=>x=-38

c: \(\Leftrightarrow3x+12-7x+21=-3-5x-2=-5x-5\)

=>-4x+33=-5x-5

=>x=-38

d: \(\Leftrightarrow-123+2x+23=x-120\)

=>2x-100=x-120

=>x=-20

e: =>-45+25+5x=16-x

=>5x-20=-x+16

=>6x=36

=>x=6

a: \(\left(2x-3\right)\left(3x^2+1\right)-6x\left(x^2-x+1\right)+3x^2-2x=10\)

\(\Leftrightarrow6x^3+2x-9x^2-3-6x^3+6x^2-6x+3x^2-2x=10\)

\(\Leftrightarrow-6x-3=10\)

=>-6x=13

hay x=-13/6

b: \(\Leftrightarrow3x^2-3x+x-2-3x^2+5x=-8-5x\)

=>3x-2=-5x-8

=>8x=-6

hay x=-3/4

c: \(\Leftrightarrow64x^3-27-64x^3+32x^2-32x^2+x=20\)

=>x-27=20

hay x=47

2: =(2x+1)^2-y^2

=(2x+1+y)(2x+1-y)

3: =x^2(x^2+2x+1)

=x^2(x+1)^2

4: =x^2+6x-x-6

=(x+6)(x-1)

5: =-6x^2+3x+4x-2

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

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

6: =5x(x+y)-(x+y)

=(x+y)(5x-1)

7: =2x^2+5x-2x-5

=(2x+5)(x-1)

8: =(x^2-1)*(x^2-4)

=(x-1)(x+1)(x-2)(x+2)

9: =x^2(x-5)-9(x-5)

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

a,  2 3 x + 5 2 x = 2 5 2 + 2 3 - 33

8x+25x = 33

33x = 33

x = 1

b,  260 : x + 4 = 5 2 3 + 5 - 3 3 2 + 2 2

260:(x+4) = 5.13–3.13

x+4 = 260:26

x+4 = 10

x = 6

c,  720 : [ 41 - 2 x - 5 ] = 2 3 . 5

41–(2x–5) = 720:40

2x–5 = 41–18

2x = 28

x = 14

d,  3 2 - 2 x - 12 + 35 = 5 2 + 279 : 3 2

7(x–12)+35 = 56

7(x–12) = 21

x–12 = 3

x = 15