Simple Simplification hopefully?

Question

Hey, i just need a bit of help with a few things that i should know but just forgot how to do, lol. I'm pretty sure you can simplify at least a few of these down, hopefully someone out there remembers it better than i do, Thanks!

(x+3) + ((2x)/(x-5))

(x+3) - ((2x)/(x-5))

(x+3) * ((2x)/(x-5))

(x+3) / ((2x)/(x-5))

and yes i know there's extra () i just put them in to make sure everyone would know what i mean b/c it's hard to write this nicely on here, Thanks Again.

Answer 1

take the LCM and simplify

((x+3) (x - 5) + 2x) / (x - 5)

= (x^2 - 15)/ (x - 5)

= x+5

Similarly others

Answer 2

Multiply your first term, (x+3), by (x-5)/(x-5) so you can get a common denominator.

That gives you [ (x+3)(x-5) + 2x ]/(x-5)

Using foil, you get: [(x^2 -5x + 3x - 15) +2x ]/(x-5)

That simplifies to: (x^2 - 15)/(x-5)

Second one is similar, with the exception you have a -2x instead of a +2x.

Third is just (x + 3)(2x)/(x-5)

Fourth uses foil again, except you need to remember how to handle compound fractions. You flip the denominator and multiply.

(x+3) * (x-5)/(2x)

Answer 3

(x + 3) + ((2x)/(x - 5))
(((x + 3)(x - 5)) + 2x)/(x - 5)
((x^2 - 5x + 3x - 15) + 2x)/(x - 5)
(x^2 - 2x - 15 + 2x)/(x - 5)
(x^2 - 15)/(x - 5)

-------------------------------------------

(x + 3) - ((2x)/(x - 5))
(((x + 3)(x - 5)) - 2x)/(x - 5)
(x^2 - 2x - 15 - 2x)/(x - 5)
(x^2 - 4x - 15)/(x - 5)

--------------------------------------------

(x + 3) * ((2x)/(x - 5))
(2x(x + 3))/(x - 5)
(2x^2 + 6x)/(x - 5)

-------------------------------------------

(x + 3)/((2x)/(x - 5))
((x + 3)/1)/((2x)/(x - 5))
((x + 3)/1)*((x - 5)/(2x))
((x + 3)(x - 5))/(2x)
(x^2 - 2x - 15)/(2x)

I was just going to say it was nice of you to separate the values. I do the same thing when i am trying to answer people's questions.