Respuesta :

Answer:

[tex]\frac{1}{(x+3)(x+1)}[/tex]

Step-by-step explanation:

given [tex]\frac{x-2}{x^2+x-6}[/tex] ÷ [tex]\frac{x^2+5x+4}{x+4}[/tex]

factor the quadratic expressions in both fractions

x² + x - 6 = (x + 3)(x - 2) and x² + 5x + 4 = (x + 4)(x + 1)

Now leave the first fraction, change division to multiplication and turn the second fraction upside down.

= [tex]\frac{x-2}{(x-2)(x+3)}[/tex] × [tex]\frac{x+4}{(x+4)(x+1)}[/tex]

In the first fraction (x - 2) cancels and in the second fraction (x + 4) cancels, leaving

[tex]\frac{1}{(x+3)(x+1)}[/tex]


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