AP Calculus Summer Work Help

[CB1101]

Could someone walk me through this problem so I can do the rest on my own? Thanks

Simplify:

X^3 - 9x / x^2 - 7x + 12

 

[JeffM]

Could someone walk me through this problem so I can do the rest on my own? Thanks

Simplify:

X^3 - 9x / x^2 - 7x + 12

\(\displaystyle X^3 - 9x/x^2 - 7x + 12 = X^3 + 9/(-x) - 7x + 12 = = X^3 + \dfrac{7x^2 -12x + 9}{-x} = X^3 - \dfrac{7x^2 - 12x + 9}{x}.\)

But I do not think that is what you meant. Learn to be careful with parentheses and capitalization

\(\displaystyle \dfrac{x^3 - 9x}{x^2 - 7x + 12}\) is what you probably meant.

Hint: Factor numerator and denominator. What does that give you? Can you simplify that?

 

[CB1101]

\(\displaystyle \dfrac{x^3 - 9x}{x^2 - 7x + 12}\) is what you probably meant.

Yes, sorry. That is actually what I meant.

I factored the numerator and denominator and came up with this:

x(x^2 - 9)
(x-4)(x-3)

I'm not sure how to simplify that.

 

[DrPhil]

Yes, sorry. That is actually what I meant.

I factored the numerator and denominator and came up with this:

x(x^2 - 9)
(x-4)(x-3)

I'm not sure how to simplify that.

Keep factoring the numerator: (x^2 - 9 ) = ..

You will find that one factor will cancel a factor in the denominator.

 

[Deleted member 4993]

Yes, sorry. That is actually what I meant.

I factored the numerator and denominator and came up with this:

x(x^2 - 9) \(\displaystyle = \displaystyle\frac{x(x^2 - 3^2)}{(x-4)(x-3)}\)
(x-4)(x-3)

I'm not sure how to simplify that.

.

 

[DrPhil]

\(\displaystyle \displaystyle\frac{x(x^2 - 3^2)}{(x-4)(x-3)}\).

What Subhotosh Kahn was calling to your attention is that you have a "difference of two squares." Did you catch that? That is a very important factoring theorem that should have a place near the top of your mind when you are factoring.

 

[CB1101]

What Subhotosh Kahn was calling to your attention is that you have a "difference of two squares." Did you catch that? That is a very important factoring theorem that should have a place near the top of your mind when you are factoring.

Alright. Is this the most simplified i can make it? x(x-3)
...............................................................(x-4)

 

[mmm4444bot]

x(x-3)
(x-4)

It looks like you cancelled the wrong factor, in the numerator. (Or, maybe your error is typographical.) :cool:

If you cannot find the mistake above, please show us what you got when you factored x^2-9.

 

[JeffM]

Alright. Is this the most simplified i can make it? x(x-3)
...............................................................(x-4)

No No No!!!!!

\(\displaystyle \dfrac{x^3 - 9x}{(x - 4)(x - 3)} =\)

\(\displaystyle \dfrac{x(x^2 - 9)}{(x - 4)(x - 3)} =\)

\(\displaystyle \dfrac{x(x + 3)(x - 3)}{(x - 4)(x - 3)} =\)

\(\displaystyle \dfrac{x(x + 3)}{x - 4}.\)