Question 1165750
<pre>
Students usually leave off parentheses to indicate numerators and denominators, so you just have to guess what they mean.  I put them
in like I assumed he meant.

{{{matrix(2,2,

lim,(2-root(3,x))/(8-x),
"x->8","")}}}

Factor 8-x this way:

{{{matrix(1,4,Let,x=y^3,then, y=root(3,x))}}}

{{{8-x=8-y^3=2^3-y^3=(2-y^"")(2^2+2y+y^3)=(2-y)(4+2y+y^3^"")=(2-root(3,x))(4+2*root(3,x)+(root(3,x))^2)}}}

Substituting:

{{{matrix(2,2,

lim,(2-root(3,x))/(8-x),
"x->8","")}}}{{{""=""}}}{{{matrix(2,2,

lim,(2-root(3,x))/(2-root(3,x))(4+2*root(3,x)+(root(3,x))^2),
"x->8","")}}}{{{""=""}}}


{{{matrix(2,2,

lim,""^""^1cross(2-root(3,x))/(cross(2-root(3,x)))(4+2*root(3,x)+(root(3,x))^2),
"x->8","")}}}{{{""=""}}}{{{matrix(2,2,

lim,1/(4+2*root(3,x)+(root(3,x))^2),
"x->8","")}}}{{{""=""}}}


{{{1/(4+2*root(3,8)+(root(3,8))^2)}}}{{{""=""}}}{{{1/(4+2(2)+2^2)}}}{{{""=""}}}{{{1/(4+4+4)}}}{{{""=""}}}{{{1/12}}}

Edwin</pre>