Answer:
[tex]\frac{ - 2(x + 6)}{ {x}^{2} - 16}[/tex]
Step-by-step explanation:
[tex] \frac{x}{ {x}^{2} - 16 } - \frac{3}{x - 4} [/tex]
[tex] = \frac{x}{ {x}^{2} - {4}^{2} } - \frac{3}{x - 4} [/tex]
Find the LCM is
[tex] {x}^{2} - {4}^{2} = (x - 4)(x + 4) [/tex]
[tex] = \frac{x - 3(x + 4)}{ {x}^{2} - {4}^{2} } [/tex]
[tex] = \frac{x - 3x - 12}{ {x}^{2} - {4}^{2} } [/tex]
[tex] = \frac{ - 2x -12 }{ {x}^{2} - 16} [/tex]
[tex] = \frac{ - 2(x + 6)}{ {x}^{2} - 16} [/tex]
