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  x = ±5

Step-by-step explanation:

Multiply by (x-1)(x+1) and you get ...

  (x+1) - (x -1) = (x -1)(x +1)/12

  24 = x^2 -1 . . . . simplify and multiply by 12

  0 = x^2 -25 . . . subtract 24

  0 = (x -5)(x +5) . . . factor the difference of squares

Values of x that make the factors 0 are x=5 and x=-5.

The solutions are x=-5 or x=5.

_____

Subtracting the right side gives an equation that has its solutions at the x-intercepts of the left-side expression. These are seen to be -5 and +5 in the attached graph.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent