Question

How do you simplify `2/(x-2) div (x-1)/(4x - 8)`?

Answer 1

`8/(x-1)`

Explanation:

Begin by factorising 4x - 8 = 4(x - 2)

fraction now becomes

`2/(x-2) ÷ (x-1)/(4(x-2))`

division of algebraic fractions is exactly the same as for numeric fractions.

`rArr color(red)(|bar(ul(color(white)(a/a)color(black)( a/b ÷ c/d = a/bxxd/c)color(white)(a/a)|)))`

so `2/(x-2) ÷ (x-1)/(4(x-2)) = 2/(x-2) xx(4(x-2))/(x-1)`

and cancelling (x-2) gives

`2/(cancel(x-2)) xx( 4cancel((x-2)))/(x-1) = 8/(x-1)`