Results 1 to 5 of 5

Math Help - Limits with fractions

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    43

    Limits with fractions

    Hi,

    I do not understand how the two limits are equal to each other. Can someone include more steps between them please?

    I do understand that the two fractions need to be subtracted from each other, therefore the denominator must be multiplied to each part of the fraction. But why do one of the 8's disappear?

    Thanks
    Attached Thumbnails Attached Thumbnails Limits with fractions-limits.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by CSG18 View Post
    Hi,

    I do not understand how the two limits are equal to each other. Can someone include more steps between them please?

    I do understand that the two fractions need to be subtracted from each other, therefore the denominator must be multiplied to each part of the fraction. But why do one of the 8's disappear?

    Thanks
    You don't understand that???!!

    You should have done enough algebra to know that

    \frac{a}{b} - \frac{c}{d} = \frac{ad-bc}{bd}

    Likewise:

    \frac{8}{(x+h)^2} - \frac{8}{x^2} = \frac{8(x^2) - 8(x+h)^{2}}{x^{2}(x+h)^{2}}

    do you understand now?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    43
    thanks, I completely understand what you wrote, but its not what the image says....

    Am I missing something, or is the image wrong?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2010
    Posts
    43
    My bad! I didn't spot that it had been factorised!








    .....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by CSG18 View Post
    thanks, I completely understand what you wrote, but its not what the image says....

    Am I missing something, or is the image wrong?
    No, the image is not wrong!

    another example: 2x-2y = 2(x-y)

    Likewise for this fraction,

    \frac{8}{(x+h)^2} - \frac{8}{x^2} = \frac{8(x^2) - 8(x+h)^{2}}{x^{2}(x+h)^{2}}

    look at the numerator:

    8(x^2) - 8(x+h)^{2} = 8({x^{2}}-(x+h)^{2}

    Clear?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 28th 2010, 09:53 AM
  2. limits with fractions (x in denominator)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 13th 2009, 07:21 AM
  3. Simplifying Fractions over fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 28th 2009, 10:20 AM
  4. simplifing fractions over fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 16th 2007, 01:57 PM
  5. summation limits in fractions
    Posted in the LaTeX Help Forum
    Replies: 13
    Last Post: November 2nd 2007, 08:02 AM

Search Tags


/mathhelpforum @mathhelpforum