((x)/8-2x)times((4-x)/2x)?

[(x/8)-2x]*[(4-x)/(2x)]; The first step to simplify this problem would be to combine (x/8) with the -2x from the first half. You can do this by making each part have a common denominator. This is a number that is a multiple of both denominators.

Lets choose 8 as our common denominator. Now we can multiply (x/8) by (1/1) to get (x)/8
Then we can multiply-2x by 8/8 to get -16x/8

Our new expression for the first two terms is now: [(x/8)-(16x/8)]=(-15x/8)
Now that we have simplified the first half, we can start multiplying


Our problem is now: [(-15x/8)]*[(4-x)/2x]
Remember that when multiplying fractions we can multiply all of the top numbers to get the new numerator and multiply all of the bottom numbers to get the new denominator which yields us:

(-15x*(4-x))/(16x) Now distribuite the (4-x) and combine like terms

(-60x+15x^2)/(16x)= (15x*(-4+x))/(16x)=(15/16)*(x-4)

=x(4-x) / ((8-2x)2x)
=(4x-x^2) / (16x-4x^2)
=4-x / 16-4x