How do you simplify $(p²-3p-28) /( p²-4p-21)$ ?

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Answer 1 · 2015-10-23T12:36:41

$(p²-3p-28) /( p²-4p-21) = color(green)((p+4)/(p+3)$

Let's look at the 2 polynomials separately

$color(red)(p²-3p-28$
$= p^2 -7p +4p - 28$
$= p(p-7) + 4(p - 7)$
$= (p-7)(p+4)$

$color(red)( p²-4p-21$
$= p^2 - 7p + 3p -21$
$= p(p-7) + 3(p-7)$
$=(p-7)(p+3)$

Hence $(p²-3p-28) /( p²-4p-21) = {cancel((p-7))(p+4)}/{cancel((p-7))(p+3)}$

$= color(green)((p+4)/(p+3)$

How do you simplify (p²-3p-28) /( p²-4p-21)(p²-3p-28) /( p²-4p-21)?