Run through the steps of this division

[cabellos6]

Homework Statement

Please could someone run through the steps of this division ((2(x-1)^2) e^-x)/(1-x)

Homework Equations

The Attempt at a Solution

is it necessary to multiply out this bracket?...im quite confused.

thanks for help

 

[quantumdude]

Not only is it not necessary to expand the product in the numerator, it is undesirable to do so. When you divide algebraic expressions, you want them to be factored. So let me ask you something, how do you simplify the following?

$$\frac{x-1}{1-x}$$

 

[cabellos6]

to be honest I am not sure... I have looked at a similar problem (x+1)/(x-1) and understand that the aim is to cancel the denominator by writing it above and + 2 to make it the numerator

therefore x - 1 + 2 / x-1

so i can see how that becomes 1 + 2/(x-1)

for some reason i do the same with this and I am not getting the correct answer.

 

[quantumdude]

to be honest I am not sure... I have looked at a similar problem (x+1)/(x-1) and understand that the aim is to cancel the denominator by writing it above and + 2 to make it the numerator

That is not a similar problem. Go back to the problem I asked you about, and factor -1 out of the denominator. What does the quotient simplify to?

 

[cabellos6]

ok so that then becomes (x-1) / (-1)(-1+x),

which becomes 1/(-1)(1)
therefore -1 ?

 

[quantumdude]

Yes. And that's a piece of the problem you posted in the beginning.

You have:

$$\frac{2(x-1)^2e^{-x}}{1-x}=\frac{2(x-1)(x-1)e^{-x}}{1-x}$$

Do you see where you can make a reduction, using what you have just figured out?

 

[cabellos6]

ok so the (x-1)(x-1)/1-x reduces to +1?

 

[quantumdude]

No. How would that happen? You just figured out that (x-1)/(1-x) reduces to -1.

 

[cabellos6]

i gather I am looking at the (x-1)(x-1)/ (-1)(-1+x) cancelling to leave -1.

then = -2e^-x ??

 

[quantumdude]

i gather I am looking at the (x-1)(x-1)/ (-1)(-1+x) cancelling to leave -1.

How are you getting that? The (-1+x) on the bottom cancels with one of the factors of (x-1) on the top. After the cancellation, there's still one left!

then = -2e^-x ??

Nope.

 

[cabellos6]

does it become -2(x-1)e^-x

(-2x + 2)e^-x

= -2xe^-x + 2e^-x

 

[quantumdude]

Yes, that's it.

 

[cabellos6]

Thanks very much. Sorry for dragging you through that.