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Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(x^2-16\right)}{\left(x^2-5x+4\right)} The numerator is AnswerThe denominator is Answer

Simplify the rational expression below When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between class=

Respuesta :

[tex]\frac{(x^2-16)}{(x^2-5x+4)}[/tex]

For the numerator:

[tex]x^2-16=(x-4)(x+4)[/tex]

For the denominator:

The factors of 4 that sum to -5 are -1 and -4, So:

[tex]x^2-5x+4=(x-1)(x-4)[/tex]

Therefore:

[tex]\frac{(x^2-16)}{(x^2-5x+4)}=\frac{(x-4)(x+4)}{(x-1)(x-4)}=\frac{x+4}{x-1}[/tex]

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