What is (x^2-4)/(12x) -: (2-x)/(4xy)?

1 Answer
Feb 15, 2016

-(x+2) y /(3)

Explanation:

(x^2-4)/(12x) div (2-x)/(4xy)

Whenever we have a complex division, may it is simpler to turn it into a mutiplication a div (b/c)= a xx (c/b):

(x^2-4)/(12x) xx (4xy)/(2-x)

We can now exchange the denominators, because multiplication is permutable:

(x^2-4)/(2-x) xx (4xy)/(12x)

Let's turn 2-x in a expression that begins by x. Doesn't have any effect, but I need it to develope the reasoning:

(x^2-4)/(-x+2) xx (4xy)/(12x)

Now, let's take the minus sign of x to outside of the expression:

-(x^2-4)/(x-2) xx (4xy)/(12x)

x^2-4 is on the form a^2-b^2, which is (a+b)(a-b):

-((x-2)(x+2))/(x-2) xx (4xy)/(12x)

Now we can cut the factors in common between numerators and denominators:

-(cancel(x-2)(x+2))/cancel(x-2) xx (4cancel(x)y)/(12cancel(x))

-(x+2) xx (4y)/(12)

Now, you only need to divide 12 by 4:

-(x+2) y /(3)