Question

How do you divide `(2x^2-2x+4)/( 2x-1)`?

Answer 1

`x-(3/2)+5/(4x-2)`

Explanation:

Polynomial division works much the same way as regular long division:

Find a value that multiplied to the first term of the denominator is equal to the first term of the numerator (sorry, formatting this is a little hard)
`(2x-1)*x=2x^2-x`

so your first term is x

next subtract the numerator by new value
`(2x^2-2x+4)-(2x^2-x)=-3x+4`

Then repeat the first term for this new value, find a value that multiplied by your (original) denominator is equal to the new value
`(2x-1)*-3/2=-3x+(3/2)`

so your second term is `-(3/2)`

subtract the numerator (from after the first subtraction) by this new value
`(-3x+4)-(-3x+(3/2))=5/2`

Finally like the remainder of normal long division you make a fraction over the divisor
`(5/2)/(2x-1)=5/(4x-2)`

This is your last term leaving you with
`x-(3/2)+5/(4x-2)`

A great resource for these sorts of problems if you can't understand my formatting: http://www.purplemath.com/modules/polydiv2.htm