Question

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

Answer 1

`(x(x-1))/(3(x+4))`

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)`