Answer:
The option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct
That is [tex]\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
Therefore [tex]\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
Step-by-step explanation:
Given problem is StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction
It can be written as below :
[tex]\frac{x}{x^2-16}-\frac{3}{x-4}[/tex]
To solve the given expression
[tex]\frac{x}{x^2-16}-\frac{3}{x-4}[/tex]
[tex]=\frac{x}{x^2-4^2}-\frac{3}{x-4}[/tex]
[tex]=\frac{x}{(x+4)(x-4)}-\frac{3}{x-4}[/tex] ( using the property [tex]a^2-b^2=(a+b)(a-b)[/tex] )
[tex]=\frac{x-3(x+4)}{(x+4)(x-4)}[/tex]
[tex]=\frac{x-3x-12}{(x+4)(x-4)}[/tex] ( by using distributive property )
[tex]=\frac{-2x-12}{(x+4)(x-4)}[/tex]
[tex]=\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
[tex]\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
Therefore [tex]\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
Therefore the option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct
That is [tex]\frac{-2(x+6)}{(x+4)(x-4)}[/tex]
