Question

Simplify fully 3x^2-6x/x^2+2x-8?

Answer 1

Have a look at https://socratic.org/help/symbols. Note the hash at the beginning and end of the 'entered' example

`(3x)/(x+4)`

Explanation:

Assumption: You mean `(3x^2-6x)/(x^2+2x-8)`

Written as: hash (3x^2-6x)/(x^2+2x-8) hash
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`color(blue)("Lets experimint with approaches.")`

`color(brown)("Consider the part: "3x^2-6x)`

factor out the common value of `3x` giving `3x(x-2)`

`color(brown)("Consider the part "x^2color(green)(+2)xcolor(magenta)(-8))`

These take a bit of practice.
Note that `(-2)xx(+4)=color(magenta)(-8) and +4-2=color(green)(+2)`

So we have:

`x^2+2x-8color(white)("d")-> color(white)("d") (x+4)(x-2)`
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`color(blue)("Lets see what happens when we put it all together")`

`(3x^3-6x)/(x^2_2x-8) color(white)("d")->color(white)("d") (3xcancel((x-2))^1)/((x+4)cancel((x-2))^1) = (3x)/(x+4)`