I am assuming that you meant "solve for x: (x^2)/(x-4) + 16/(4-x)." Unfortunately, this is an expression, not an equation. Check that you have copied down this problem correctly.
I note right away that the 2nd term could be re-written as - 16/(x-4). The advantage to this re-write is that the terms now have the same denominator. You could combine these 2 terms as follows: (x^2)/(x-4) - 16/(x-4), or
x^2 - 16 ------------ x-4 (x-4)(x+4) The numerator factors easily; the correct result is -------------- x-4
Simplifying, we get x+4. Note: this cannot be solved for x; it's just an expression. This result is correct ONLY for x not equal to 4. (Why?)
Now look at the 2nd problem. Here you do have an equation involving fractions. The LCD is (3)(4)=12. Multiply all three terms of this equation by 12 to obtain
3(5x-2) -4(4x-5) = 12(1)=12.
Then 15x-6-16x+20=12, or -6+20-12=16x-15x = x. Then x=2. You MUST check this result via substituion before accepting it as the solution of this problem.
