Solve 5 / (x - 4) - 3 / (x + 4) = 6 / (x^2 - 16)?

5 / (x - 4) - 3 / (x + 4) = 6 / (x^2 - 16)

multiply both side in (x - 4) * (x + 4) :

5 * (x + 4) - 3 * (x - 4) = 6

expand equation :

5 * x + 20 - 3 * x + 12 = 6
2 * x = - 26
x = -13

5 / (x - 4) - 3 / (x + 4) = 6 / (x^2 - 16)
Multiplying both sides with the LCM of the denominators, we get
5(x+4) - 3(x - 4) = 6
Now expanding
5x +20 -3x +12 =6
or 2x = 6 - 32
or x= - 26/2
or x= -13

Put all terms over the common denominator x^2-16:
5(x+4)/(x^2-16) -3(x-4)/(x^2-16) = 6(x^2-16)
Simplify the numerators:
(5x+20 -3x +12)/(x^2-16) = 6/(x^2-16)
Set numerators = to each other since denominators are =
2x+32 = 6
Simple algebra from here
2x = -26
x = -13

5 (x + 4) - 3 (x - 4) = 6

5x + 20 - 3x + 12 = 6

2x = - 26

x = - 13

5/(x - 4) - 3/(x + 4) = 6/(x^2 - 16)
(x - 4)(x + 4)[5/(x - 4) - 3/(x + 4)] = (x - 4)(x + 4){6/[(x + 4)(x - 4)]}
5(x + 4) - 3(x - 4) = 6
5*x + 5*4 - 3*x + 3*4 = 6
5x + 20 - 3x + 12 = 6
5x - 3x = 6 - 20 - 12
2x = -26
x = -26/2
x = -13

5 / (x - 4) - 3 / (x + 4) = 6 / (x^2 - 16)
5 / (x - 4) - 3 / (x + 4)=6/[(x-4)(x+4)]
multiply across by [(x-4)(x+4)]:
5(x+4)-3(x-4)=6
5x+20-3x+12=6
2x=-26
x=-13

x²-16=(x+4)(x-4)
5/(x-4)-3/(x+4)=6/(x+4)(x-4)
Multiply both sides by (x+4)(x-4)
5(x+4)-3(x-4)=6
5x+20-3x+12=6
2x+32=6
2x=-26
x=-13

5/(x - 4) - 3/(x + 4) = 6/(x^2 - 16) (factor denominator)
5/(x - 4) - 3/(x + 4) = 6/((x + 4)(x - 4)) (multiply both sides by (x + 4)(x - 4))
5(x + 4) - 3(x - 4) = 6 (distribute)
5x + 20 - 3x + 12 = 6 (combine like terms)
2x + 32 = 6 (subtract 32 from both sides)
2x = -26 (divide both sides by 2)
x = -13 <===ANSWER