Factoring Help? x_x;?

Question

Here are a few examples:
2x / x + 4 (multiply) x - 1 / 3

and..

3y + 15 / y (divide) y + 5 / y

and..

2x + 1 / x + 2 (add) 3 / x + 2

=| Can someone show how do it step by step?

Answer 1

(2x/x + 4) * (x - 1/3)
= 2x(x - 1)/3(x + 4)

Further factoring is not possible
--------------- -------------------- ------------------- --------------
(3y + 15/y)/(y + 5/y)
= y(3y + 15)/y(y + 5)

Cancel out the y in numerator and denominator. We are left with:
3y + 15/y + 5
= 3(y + 5)/(y + 5)
= 3
------------ ----------------- ----------------- ----------------- --------------

(2x + 1/x + 2) + (3/x + 2)
= 2x + 1 + 3/x + 2
= 2x + 4/x + 2
= 2(x + 2)/x + 2
= 2
---------- ---------- ---------- ---------- --------- ----------- ----------

Answer 2

Let's start with the first one:

2x / (x+4) * (x-1)/3 [I hope this is what you meant]

Multiplying is easy, 'cause you can just multiply the numerators with each other and the denominators with each other.

2x / (x+4) * (x-1)/3 =

2x(x-1)
_____

3(x+4)


This can't really be factored anymore.



With division it's the exact same, except before you multiply the numerators and denominators, be sure to flip the second fraction. Instead of using (y+5)/y, use y/(y+5).



With addition things are much more complicated.

(2x + 1)/(x+2) + 3/(x+2)

Or maybe not... normally you'd do this trick to make both denominators the same. But here they are already the same. So just add across the top and keep the denominator the same

2x + 1 + 3
________
x+2



Hope this helps.