Add. Express your answer in simplest form.?

Question

Add. Express your answer in simplest form.

2x 4
-------------------- + ----------------
x^2 + 15x + 54 x+8

i mean 2x/x^2 + 15x + 54 + 4/x+8



Help please!!!

Answer 1

2x / (x^2 + 15x + 54) + 4 / (x + 8) =
(2x (x + 8) + 4(x^2 + 15x + 54)) / [(x + 8)(x^2 + 15x + 54)] =
(2x^2 + 16x + 4x^2 + 60x + 216) / [(x + 8)(x^2 + 15x + 54)] =
(6x^2 + 76x + 216) / [(x + 8)(x^2 + 15x + 54)] =
6(x^2 + (38/3)x + 36) / [(x + 8)(x^2 + 15x + 54)] =
6(x^2 + (38/3)x + (38/6)^2 - (38/6)^2 + 36) / [(x + 8)(x^2 + 15x + 54)] =
6[(x + 19/3)^2 - 381/9 + 324/9) / [(x + 8)(x^2 + 15x + 54)] =
6[(x + 19/3)^2 - 57/9) / [(x + 8)(x^2 + 15x + 54)] =
There are no similar factors, so simplest form is
2(3x^2 + 38x + 108) / [(x + 8)(x + 6)(x + 9)]

Answer 2

do you mean 2x/x^2 + 15x + 54 + 4/(x+8) ?
notice you have 2 different denominators first term and last term. need to make this the LCD (least common denominator)
[x^2(x+8)] needs to be under every term
first term multiply (x+8)/(x+8) and last term multiply (x^2/x^2)
[2x*(x+8)]/[x^2(x+8)] + [15x*x^2(x+8)]/[x^2(x+8)]
+ [54 * [x^2(x+8)]]/[x^2(x+8)] + [4*x^2]/[x^2(x+8)]
now all 4 terms are over a common denominator [x^2(x+8)],
lets call this LCD for ease of writing in this wonderful test format
[2x*(x+8) + 15x*x^2(x+8) + 54*x^2(x+8) + 4x^2] / LCD
[(2x^2+16x)+(15x^4+120x^3)+(54x^3+432x^2)+(4x^2)]/LCD
collect like terms and you get
[25x^4 + 174x^3 + 438x^2 + 16x]/LCD
you can factor out an x top and bottom so
[25x^3 + 174x^2 + 438x + 16]/[x^2+8x)] should be the answer
take your time stepping through this
there is a lot of detail