# How do you simplify #(2x) /( x + 4) div (6)/(x-1)#?

##### 1 Answer

May 15, 2016

#### Explanation:

When we have a fraction divided by another fraction. Then leave the first fraction and multiply by the 'reciprocal' (flip the fraction over) of the second fraction.

In general:

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

#rArr(2x)/(x+4)÷6/(x-1)=(2x)/(x+4)xx(x-1)/6# Now that we have multiplication we can cancel any factors on the numerators with any common factors on the denominators.

#rArr(cancel(2)^1 x)/(x+4)xx(x-1)/cancel(6)^3=x/(x+4)xx(x-1)/3# We can now rewrite the product of these fractions as a single fraction.

In general :

#color(red)(|bar(ul(color(white)(a/a)color(black)(a/b xxc/d=(ac)/(bd))color(white)(a/a)|)))#

#rArrx/(x+4)xx(x-1)/3=(x(x-1))/(3(x+4)#