Question

How do you simplify `(y-x)/(12x^2-12y^2)`?

Answer 1

`-1/(12(x+y))`

Explanation:

`"factor out "color(blue)"common factor" " of 12 in numerator"`

`rArr(y-x)/(12(x^2-y^2))`

`x^2-y^2" is a "color(blue)"difference of squares"` and factorises in general

`• a^2-b^2=(a-b)(a+b)`

`rArr(y-x)/(12(x-y)(x+y))`

`"factor out " -1" in the numerator"`

`rArr(-cancel((x-y)))/(12cancel((x-y))(x+y))`

`=-1/(12(x+y))to(x!=-y)`