Question 44076
1.
make sure the denominators are identical
{{{1/3+2=1/3+6/3=7/3}}}

2.
Firstly, expand your brackets.
Remember the word FOIL. It stands for: Firsts, Outers, Inners, Lasts. 
Take (a+b)(c+d)for example add the products of F.O.I.L:
{{{(a+b)(c+d)= ac + ad + bc + bd}}} 
In your question 
a=t
b=-3
c=t
d=5
So:
{{{(t-3)(t + 5)=t^2+5t-3t-15=9}}}
Now rearrange to give zero on the right hand side of a quadratic expression.
{{{t^2+5t-3t-24=0}}}
{{{t^2+2t-24=0}}}
Use the quadratic solver {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
where
a=1
b=2
c=-24
Now:
{{{x = (-2 +- sqrt( 2^2-4*1*(-24) ))/(2*1) }}} 
{{{x = (-2 +- sqrt( 4+56 ))/2 }}} 
{{{x = -1 +- sqrt( 60)/2 }}}

3.
{{{(x-3)^2 + (x+2)^2=17}}}
Simplify:
{{{(x-3)(x-3) + (x+2)(x+2)=17}}}
using FOIL:
{{{(x^2-6x+9)+(x^2+4x+4)=17}}}
{{{2x^2-2x+13=17}}}
{{{2x^2-2x-4=0}}}
Now using the quadrastic solver again where
a=2
b=-2
c=-4
{{{x=1 +- sqrt(36)/2}}}

4.
The method for solving cubic equations is very long. refer to http://www.sosmath.com/algebra/factor/fac11/fac11.html
for an explanation and examples

I hope this helps 
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk