Differentiation techniques, help!!

[sondang]

Hi I need help with two problems that are similar to each other

1) Find the x-coordinates of the points on the curve y = (x^2 − 1)/x at which the gradient of the curve is 5.

2) Find the gradient of the curve y = (2x − 4)/x^2 at the point where the curve crosses the x-axis.

I just don't know how to approach the problem

Help greatly appreciated thanks!

[pi]

Hints:
1)  y = (x^2 − 1)/x = x^2/x - 1/x = x- 1/x

2) Break it up as above

Post back if you still need a hand

[sondang]

I'm already stuck haha, I don't know what to do after simplifying it

[Lasercookie]

I'm already stuck haha, I don't know what to do after simplifying it

For 1:

You can differentiate it after you've simplified it



(you'll get pretty quick at this, you should eventually be able to do most of these steps in your head).

You can solve now. You'll get the x-values out from there.

For 2:
2) Find the gradient of the curve y = (2x − 4)/x^2 at the point where the curve crosses the x-axis.
You'll want to find that point and then sub that into the derivative.

[sondang]

I'm already stuck haha, I don't know what to do after simplifying it

For 1:

You can differentiate it after you've simplified it



(you'll get pretty quick at this, you should eventually be able to do most of these steps in your head).

You can solve now. You'll get the x-values out from there.

For 2:
2) Find the gradient of the curve y = (2x − 4)/x^2 at the point where the curve crosses the x-axis.
You'll want to find that point and then sub that into the derivative.

Thanks for the help!!! I got the answers correct