Someone help me combine and simplify this problem? please!!!?

Question

2 / x+3 + x / x+5

This is all one problem...2 over x+3 + x over x+5

Answer 1

x+3/x+5

or x+3 (all over) x+5

Answer 2

I think it is (x^2+5x+10)/(x+3)(x+5)

Answer 3

These are fractions.  The first thing you need to do is find a common denominator.  First you look for common factors between the 2 denominators (x + 3) and (x + 5).  None.  OK, then just multiply them together to get the common denominator

(x + 3) (x + 5) = x² + 3x + 15

Now set up the fractions so they both have this same denominator.

What do you need to multiply (x + 3) by in order to get x² + 3x + 15?

You multiply by (x + 5).  You have to multiply both numerator and denominator:

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

(2x + 10) / (x² + 3x + 15)

Now do the same for the 2nd term.  Multiply both top & bottom by (x + 3)

x (x + 3) / (x + 3) (x + 5)

(x² + 3x) / (x² + 3x + 15)

Now add the two terms together

(2x + 10) / (x² + 3x + 15) + (x² + 3x) / (x² + 3x + 15) =

(x² + 2x + 3x + 10) / (x² + 3x + 15) =

(x² + 5x + 10) / (x² + 3x + 15)

Now you have to factor both denominator & numerator and see if there are any common factors in order to reduce the fraction.

Since (x² + 5x + 10) can't be factored, we're done.

Answer 4

[2 / (x + 3) ] + [ x / (x + 5) ] =

[(2(x + 5) / (x+ 3)(x + 5)] + [ x (x + 3) / (x + 3)(x + 5)] =

(2x + 10 + x^2 + 3x ) / (x + 3)(x + 5) =

(x^2 + 5x + 10) / (x + 3)(x + 5) =

(x^2 + 5x + 10) / (x^2 + 8x + 15)