Solve the equation?

Question

(x / x-3) + (x / x +3) = (18 / x^2 -9) I know it looks kind of confusing

Answer 1

(x / x-3) + (x / x +3) = (18 / x^2 -9)
get the least commnon denominator on the left side (X^2-9)
do this by multiplying (x / x-3) by (x+3)/(x+3)
then multiplying (x / x +3) by (x-3)/(x-3)
now,
(x^2+3x)/(X^2-9) + (X^2 -3X)/(X^2-9) = (18/X^2-9)
Multiply both sides by (X^2-9) to get rid of denominators
then,
X^2+3X + X^2 - 3X = 18
Simplify
2 X^2 = 18
X^2 = 9
X = 3

Answer 2

(x / x-3) + (x / x +3) = (18 / x^2 -9)

Find a common denominator.
(x-3) * (x+3) = (x^2 - 9)

Thus, you can rewrite the fraction:
(x(x+3) / x^2 -9) + (x (x-3)/ x^2 -9) = (18 / x^2 -9)

Simplify:
(x^2 + 3x + x^2 - 3x) / (x^2 - 9) = 18 / (x^2 - 9)
(2x^2) / (x^2 - 9) = 18 / (x^2 - 9)

Multiply both sides by x^2 - 9:
2x^2 = 18
x^2 = 9
x = 3 (solution!)

Answer 3

Factor the "x^2-9"

(x/x-3)+(x/x-3)=18/(x+3)(x-3)

Times all the terms by (x+3)(x-3)

x(x+3)+x(x-3)=18

Expand and collect terms

2x^2=18

Divide both sides by 2

x^2=9

Take the square root of both sides

x=3

Answer 4

(x / x-3) + (x / x +3) = (18 / x^2 -9)
a^2-b^2=(a-b)(a+b) so
x^2 -9=(x-3)(x+3)
(x / x-3) + (x / x +3)= (18/( x-3)(x+3))
multiply both sides by (x-3)(x+3)
x(x+3)+x(x-3)=18
x^2+3x+x^2-3x=18
2x^2-18=0
x^2-9=0
(x-3)(x+3)=0
x-3=0 then x=3
or
X+3=0 then x=-3