You can
put this solution on YOUR website! Please show me how to do long division this way!
x² - 49y²
——————————— ÷ (x² - 7xy)
6x² + 42y
This isn't long division. It's simplifying by
"factoring and cancelling":
x² - 49y²
——————————— ÷ (x² - 7xy)
6x² + 42y
Write the second fraction over 1
x² - 49y² x² - 7xy
——————————— ÷ ——————————
6x² + 42y 1
Invert the second fraction and change to multiplication:
x² - 49y² 1
——————————— × ——————————
6x² + 42y x² - 7xy
Factor the upper left numerator: x² - 49y² = (x - 7y)(x + 7y)
Factor the lower left denominator: 6x² + 42y = 6(x² + 7y)
Factor the lower right denominator: x² - 7xy = x(x - 7y)
(x - 7y)(x + 7y) 1
—————————————————— × ——————————
6(x² + 7y) x(x - 7y)
Indicate the multiplication of the numerators and
the denominators and write as a single fraction:
(x - 7y)(x + 7y)
——————————————————————
6(x² + 7y)x(x - 7y)
Write the x next to the 6 as it is customary to write
shorter factors first:
(x - 7y)(x + 7y)
——————————————————————
6x(x² + 7y)(x - 7y)
Cancel the (x - 7y)'s
1
(x - 7y)(x + 7y)
——————————————————————
6x(x² + 7y)(x - 7y)
1
(x + 7y)
——————————————
6x(x² + 7y)
Caution: Do not try to cancel the remaining parenthetical
factors, because they are not exactly alike, since the x is
squared in the bottom but not in the top and you cannot cancel
terms between numerator and denominator. So the only thing
you can do is erase the parentheses in the top:
x + 7y
——————————————
6x(x² + 7y)
Edwin
AnlytcPhil@aol.com