1. ## 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

2. Originally Posted by CSG18
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

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

Likewise:

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

do you understand now?

3. thanks, I completely understand what you wrote, but its not what the image says....

Am I missing something, or is the image wrong?

.....

5. Originally Posted by CSG18
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: $\displaystyle 2x-2y = 2(x-y)$

Likewise for this fraction,

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

look at the numerator:

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

Clear?