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

##### 1 Answer

Apr 18, 2016

#### 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) #