Find the area of the rectangle with a length of 2x+2/x-4 and the width of 3x-12/x^2+6x+5

We're trying to evaluate a fractional expression here:


The first thing to do, is factor everything we can. The quadratic factors to (x + 1)(x+5) and the expression above that factors to 3(x - 4). 2x + 2 factors to 2(x + 1).


It looks a little complicated now, but if we combine the two we can cancel some stuff.



Still looking complicated, but look, we have (x+1) and (x+4) on the top and the bottom, that means they don't matter and we can get rid of them:



Tada! The area is 6/(x+5). We'd need to know x to go any further!

Need any more explanation?

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°