How do you divide $(7x-5x^2 – 3+6x^2) /( 2x-1)$ ?

Question

1498 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-26T22:38:58

$x/2 + 15/4 + 3/(4(2x-1))$

Given: $(7x-5x^2 - 3 + 6x^2)/(2x-1)$

First add like terms in the numerator: $(x^2+7x-3)/(2x-1)$

Long division:

step 1. $"What" xx 2x = x^2?: " "1/2x$

$" "1/2 x$
$" "2x-1 |bar(x^2 + 7x - 3)$
$" "ul(x^2 - 1/2x)$

$" "$ To subtract, change the $7$ to $7/1 xx 2/2 = 14/2$ :

$" "1/2 x$
$" "2x-1 |bar(x^2 + 14/2x - 3)$
$" "ul(x^2 - 1/2x)$
$" " 15/2x - 3$

step 2. $"What" xx 2x = 15/2x?: " "(15x)/4 xx (2x)/1 = (30x)/4 = (15x)/2$

$" "1/2 x + 15/4$
$" "2x-1 |bar(x^2 + 14/2x - 3)$
$" "ul(x^2 - 1/2x)$
$" " 15/2x - 3$
$" "ul(15/2x - 15/4)$

$" "$ To subtract, change the $-3$ to $-3/1 xx 4/4 = -12/4$ :

$" "1/2 x + 15/4$
$" "2x-1 |bar(x^2 + 14/2x - 3)$
$" "ul(x^2 - 1/2x)$
$" " 15/2x - 12/4$
$" "ul(15/2x - 15/4)$
$" "3/4$

The remainder $= 3/4/ (2x-1) = 3/(4(2x-1))$

So, $(x^2+7x-3)/(2x-1) = x/2 + 15/4 + 3/(4(2x-1))$

How do you divide (7x-5x^2 – 3+6x^2) /( 2x-1) (7x-5x^2 – 3+6x^2) /( 2x-1)?