How do I simplify: 3p^2-6p-45/p^2-p-20 divided by 2p^2+2p-24/2p^2-8p+6

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`[(3p^2-6p-45)/(p^2-p-20)]/[(2p^2+2p-24)/(2p^2-8p+6)]`

`= [(3p^2-6p-45)/(p^2-p-20)]xx[(2p^2-8p+6)/(2p^2+2p-24)]`

 

Now we have to factor each polynomial.

`3p^2-6p-45`

`= 3(p^2-2p-15)`

`= 3(p^2-5p+3p-15)`

`= 3[p(p-5)+3(p-5)]`

`= 3(p-5)(p+3)`

 

`p^2-p-20`

`= p^2-5p+4p-20`

`= p(p-5)4+4(p-5)`

`= (p-5)(p+4)`

 

`2p^2-8p+6`

`= 2(p^2-4p+3)`

`= 2(p^2-3p-p+3)`

`= 2[p(p-3)-1(p-3)]`

`= 2(p-3)(p-1)`

 

`2p^2+2p-24`

`= 2(p^2+p-12)`

`= 2(p^2+4p-3p-12)`

`= 2[p(p+4)-3(p+4)]`

`= 2(p+4)(p-3)`

 

`[(3p^2-6p-45)/(p^2-p-20)]/[(2p^2+2p-24)/(2p^2-8p+6)]`

`= [(3p^2-6p-45)/(p^2-p-20)]xx[(2p^2-8p+6)/(2p^2+2p-24)]`

`= (3(p-5)(p+3))/((p-5)(p+4))xx(2(p-3)(p-1))/(2(p+4)(p-3))`

`= (3(p+3)(p-1))/(p+4)^2`

 

So the simplfied answer is;

`[(3p^2-6p-45)/(p^2-p-20)]/[(2p^2+2p-24)/(2p^2-8p+6)] = (3(p+3)(p-1))/(p+4)^2`

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