how do i reduce this? (1/x)-(2/x^2)/(2x-4/x^5)?

Question

i know it looks crazy..
but i really need help with it...

Answer 1

(1/x)-(2/x^2)
=1*x-2/x^2
=x-2/x^2
2x-4/x^5
=2(x-2)/x^5
hence the given expression
=(x-2)/x^2 X x^5/2(x-2)
=x^(5-2)/2 [elliminating x-2 from both the numerator and denominator]
=x^3/2 ans

Answer 2

Hi Mercedes,

Okay, we have

(1 / x) - (2·/x^2) / (2·x-4 / x^5)?

First, let's do the second expression. When we divide two fractions, we invert and multiply, just like in grade school. So, we have

(2·/x^2) / (2·x-4 / x^5) = (2·/x^2)·x^5 / (2·x -4)

which gives us

2·x^3 / (2·x -4)

So, going back into our original equation, we have

******************************************
*
*

(1 / x) - (2·x^3 / (2·x -4)) *

*
*
*******************************************
Multiplying the left side by (2·x -4) / (2·x -4) gives

(2·x -4) / x·(2·x -4) .

Multiplying the right side by x / x gives

2·x^4 / x· (2·x -4)

So, subtracting, we get

((2·x -4) - 2·x^4) / x·(2·x - 4)

You should check my answer carefully for any slippery errors. They are very easy to make in problems such as these.

I hope this helps,


* Addenum - Up above you'll see an answer surrounded by stars. I fired up a program, typed in your query, and got the same answer as the one I did by hand in the box above.

So, I guarantee that answer to be correct (assuming I read your problem correctly). The stuff below is subject to the slippery errors mentioned elsewhere here.

Still more Addena: You must do the division of the fractions first, meaning that you must solve

(a / b) / (c / d)

before you do anything else.

James :-)

Answer 3

Firstly look at the first part of the equation:
(1/x)-(2/x^2)

In order to add these two, you need to have a common denomemator. In this case x^2 is the common d.
So in order to have 1/x with a common d of x^2 you multiply the top and bottom by x.

new equation
(x/x^2)-(2/x^2) so when you add these two you now have
(x-2)/x^2

Secondly when you divide fractions, you can multiply the reciprocal.

eg. (1/x) / (2/x) = (1/x)*(x/2)

So with your equation [(x-2)/x^2]/[(2x-4)/x^5]
you can multiple [(x-2)/x^2]*(x^5)/(2x-4)
when you do the multiplication the final answer is:

X^3/2

Answer 4

I don't know how your teacher wrote it exactly, but i think its this way:
(1/x)-(2/x^2)/(2x-4/x^5)
((x-2)/x^2)*(x^3/2x-4) Note: 2x-4= 2(x-2), so symplify in the next

((x-2)x^3)/2(x-2) = (x^3)/2

I hope i did wrote it right
Good luck

Answer 5

(1/x)-(2/x^2)/(2x-4/x^5)
= 1/x - (2/x^2)/(2x^6-4x^5)/x^5
=1/x -(2/x^2)(x^5/(2x^6-4x^5)
=1/x - (2/x^2)(x^5/2x^5(x-1)
1/x- 1/(x^2(x-1)
= (x(x-1) -1)/(x^2(x-1))
= (x^2-x-1)/(x^3-x^2)