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Answer :

Loneguygo

[tex]~~~~\dfrac{12}{x^2 -49} \cdot \dfrac{x^2+9x+14}{9}\\\\\\=\dfrac{4}{x^2 -7^2}\cdot \dfrac{x^2 + 7x +2x +14}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)} \cdot \dfrac{x(x+7)+2(x+7)}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)}\cdot \dfrac{(x+7)(x+2)}{3}\\\\\\=\dfrac{4(x+2)}{3(x-7)}[/tex]

Chetankachanago

Answer:

[tex]\frac{4(x + 2)}{3(x - 7)}[/tex]

Step-by-step explanation:

Hello!

We can simplify this by factoring, and cross reducing.

Simplify

  • [tex]\frac{12}{x^2 - 49} * \frac{x^2 + 9x + 14}{9}[/tex]
  • [tex]\frac{12}{(x+7)(x - 7)} * \frac{(x + 2)(x + 7)}{9}[/tex]
  • [tex]\frac{12(x + 2)}{9(x - 7)}[/tex]
  • [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]

The final simplified form is [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]

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