Well, for the first question you need to simplify. The two fractions on the left-hand side both have terms in (x-2) so if you multiply the whole thing by (x-2), you get:
1 + 2x / (x - 8) = x(x - 2) / 2(x - 8)
Now you have (x-8) as a term on both sides so multiply by (x-8) to get:
(x - 8) + 2x = x(x - 2) / 2
Multiply both sides by two to get rid of all fractional quantities:
2(x - 8) + 4x = x(x - 2)
Expand the brackets:
2x - 16 + 4x = x² - 2x
Rearrange to be a standard quadratic equation:
x² - 8x + 16 = 0
You can use the quadratic equation solver at this point but your spidey sense should be jangling at what two numbers can add up to -8 and multiply together to make 16. Minus four and minus four. The only root of the equation is thus 4.
If you plug 4 back into your original equation, it is:
1/2 - 8/8 = -4/8
Simplifying:
-1/2 = -1/2
Result!
I'll let you do the second one on your own (best way of learning). Because it's probably going to expand to a trinomial, you are looking for a term (including m) which both sides can be divided by, thus pulling it back down to a quadratic (which you know you can solve).
