Differentiation structured questions

Hey,

I need help with some questions that I have been stuck with on my crash course to teach myself calculus before school starts.

1) If $\displaystyle y = x +\sqrt{x^2 -9} $ , show that

$\displaystyle \displaystyle (x^2 -9) \dfrac{d^2y}{dx^2} + x \dfrac{dy}{dx} - y = 0 $

I have tried to solve for the derivatives of y and I derived extremely complicated fractions with powers of 3/2 and such and I cannot simplify the equation to = 0.

2)

a) $\displaystyle \dfrac {d}{dx} \dfrac{3x-4}{x+7} = \dfrac {25}{(x+7)^2}$ (found)

b) Using your answer in (a) , differentiate the following with respect to x

$\displaystyle \displaystyle y = sin(\dfrac{3x-4}{x+7})^8 $

For this, I am unsure of what to let be u so that I can use the chain rule in the form

$\displaystyle \dfrac{du}{du} \, \dfrac{du}{dx} $ or $\displaystyle \dfrac{dsinu}{du} \, \dfrac{du}{dx} $

I have dealt with trigo functions like sin^8(x) and sin(8x) but never in the form that the question gave (8th power only applies to the fraction and not the whole function) and I do not know how to proceed.

Any help at all is appreciated :)