Question

Simplify the following expression, show your work

Answer 1

how will I solve this? I have to show all the steps and I dont even know where to begin

Answer 2

Thanks @Sjano for replying

Answer 3

=1/3 (2 x^2-32) (x/(x-4)+6/(x+4))
plot in a graph or calculate it to get the 0 points, which are -12 and +2
Which would make it:
2/3 (x-2) (x+12) = 0

Answer 4

Thanks for the answer i gave u a medal but I needed step by step or I will not give full points THANK you any how

Answer 5

Or you can derivate it:

Possible derivation:
d/dx(1/3 (2 x^2-32) (x/(x-4)+6/(x+4)))
| Factor out constants:
= | 1/3 (d/dx((2 x^2-32) (x/(x-4)+6/(x+4))))
| Use the product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u = 2 x^2-32 and v = x/(x-4)+6/(x+4):
= | 1/3 ((2 x^2-32) (d/dx(x/(x-4)+6/(x+4)))+(x/(x-4)+6/(x+4)) (d/dx(2 x^2-32)))
| Differentiate the sum term by term and factor out constants:
= | 1/3 ((x/(x-4)+6/(x+4)) (2 (d/dx(x^2))+d/dx(-32))+(2 x^2-32) (d/dx(x/(x-4)+6/(x+4))))
| Differentiate the sum term by term and factor out constants:
= | 1/3 ((2 x^2-32) (d/dx(x/(x-4))+6 (d/dx(1/(x+4))))+(x/(x-4)+6/(x+4)) (2 (d/dx(x^2))+d/dx(-32)))
| The derivative of -32 is zero:
= | 1/3 ((x/(x-4)+6/(x+4)) (2 (d/dx(x^2))+0)+(2 x^2-32) (6 (d/dx(1/(x+4)))+d/dx(x/(x-4))))
| Use the quotient rule, d/dx(u/v) = (v ( du)/( dx)-u ( dv)/( dx))/v^2, where u = x and v = x-4:
= | 1/3 ((2 x^2-32) (6 (d/dx(1/(x+4)))+((x-4) (d/dx(x))-x (d/dx(x-4)))/(x-4)^2)+2 (x/(x-4)+6/(x+4)) (d/dx(x^2)))
| The derivative of x^2 is 2 x:
= | 1/3 ((2 x^2-32) (6 (d/dx(1/(x+4)))+((x-4) (d/dx(x))-x (d/dx(x-4)))/(x-4)^2)+2 (x/(x-4)+6/(x+4)) (2 x))
| Differentiate the sum term by term:
= | 1/3 ((2 x^2-32) (((x-4) (d/dx(x))-x (d/dx(-4)+d/dx(x)))/(x-4)^2+6 (d/dx(1/(x+4))))+4 x (x/(x-4)+6/(x+4)))
| Use the chain rule, d/dx(1/(x+4)) = d/( du)1/u ( du)/( dx), where u = x+4 and d/( du)1/u = -1/u^2:
= | 1/3 ((2 x^2-32) (6 (-(d/dx(x+4))/(x+4)^2)+((x-4) (d/dx(x))-x (d/dx(-4)+d/dx(x)))/(x-4)^2)+4 x (x/(x-4)+6/(x+4)))
| The derivative of x is 1:
= | 1/3 ((2 x^2-32) ((x (-(d/dx(-4)+d/dx(x)))+x-4)/(x-4)^2-(6 (d/dx(x+4)))/(x+4)^2)+4 x (x/(x-4)+6/(x+4)))
| Differentiate the sum term by term:
= | 1/3 ((2 x^2-32) ((x (-(d/dx(x)+d/dx(-4)))+x-4)/(x-4)^2-(6 (d/dx(4)+d/dx(x)))/(x+4)^2)+4 x (x/(x-4)+6/(x+4)))
| The derivative of -4 is zero:
= | 1/3 ((2 x^2-32) ((x (-(d/dx(x)+0))+x-4)/(x-4)^2-(6 (d/dx(x)+d/dx(4)))/(x+4)^2)+4 x (x/(x-4)+6/(x+4)))
| The derivative of 4 is zero:
= | 1/3 ((2 x^2-32) ((x (-(d/dx(x)))+x-4)/(x-4)^2-(6 (d/dx(x)+0))/(x+4)^2)+4 x (x/(x-4)+6/(x+4)))
| The derivative of x is 1:
= | 1/3 ((2 x^2-32) (-(6 (d/dx(x)))/(x+4)^2-4/(x-4)^2)+4 x (x/(x-4)+6/(x+4)))
| The derivative of x is 1:
= | 1/3 ((2 x^2-32) (-6/(x+4)^2-4/(x-4)^2)+4 x (x/(x-4)+6/(x+4)))

Which should equal an other shortened answer if i haven't forgotten something
(You have to do somethings by yourself. Hint: (number(x+ other number)) * 1/3