Simplify [5/(x-6)] - [4/(x+3)] = (x+39) / (x^2-3x-18)?

Answer 1

x^2-3x-18=(x-6)(x+3)
so the whole thing can be simplified to:
5(x+3)-4(x-6)=x+39
5x+15-4x+24=x+39
x+39=x+39
so x can equal anything except 6 and -3.

Answer 2

(x-6)*(x+3) = (x^2-3x-18), so that is your common denominator. the first expression needs to be multiplied by (x+3)/(x+3), and the second (x-6)/(x-6), so the new problem is (5x + 15 - 4x + 24 = x + 39) this just simplifies to x + 39 = x + 39, so any value of x (other than 6 or -3, which make the denominator 0) will work. Try 21

5/15 + 4/24 = 60/ (441- 63 - 18)

1/3 - 1/6 = 60/360

true.

Answer 3

5/(x-6)-4/(x+3)=(x+39)/(x^2-3x-18)

or(5x+15-4x+24)/(x-6)(x+3)=(x+39)/(x-6)(x+3)
(after factorising the denominator)
or (x+39)/(x-6)(x+3)=(x+39/(x-6)(x+3)
if x<>6or x<>-3, we can cancel the factors (x-6)(x+3) from both sides of the equation and are left with
x+39=x+39

Answer 4

23

Answer 5

[5x - 30] - [4x + 12] = (x + 39) / (x - 3) (x + 6)
(x - 42)(x - 3)(x + 6) = x + 39
x^3 - 3x + 6x + 6x - 42x -3x - 42x + 126 + 252 + 12 = x + 39
x^3 + 79x + 429 = 0

i think that's right

oh dear, just realised i read it wrong - oops

Answer 6

LHS
5.(x + 3) - 4.(x - 6) / [ (x - 6).(x + 3)]
(x + 39) / [ (x - 6).(x + 3) ]
RHS
(x + 39) / [ (x - 6).(x + 3) ]

Answer 7

[5/(x-6)] - [4/(x+3)]
=[5(x+3)]/[(x-6)(x+3)]- [4(x-6)]/[(x-6)(x+3)]
=[(5x+15)-(4x-24)]/[(x-6)(x+3)]
=[5x+15-4x+24]/[x^2-3x-18]
=(x+39) / (x^2-3x-18)#

Answer 8

after simplification of the whole,
we get x=-23/60

Answer 9

This one is simple, just ask someone on Yahoo answers.

Answer 10

in it's simplest form... this is just a bunch of numbers