With my algebra homework.

1.) what is the wuotient in simplified form? state any restrictions on the variable. (x^2-16/x^2+5x+6) / (x^2+5x+4/x^2-2x-8)

2.) simplify the sum
(7/a+8) + (7/a^2-64)

3.) simplify the difference
(a^2-2a-3/a^2-9a+18) - (a^2-5a-6/a^2+9a+8)

4.) simplify the complex fraction

(4/x+3) / ((1/x)+3)

5.) solve the equation. check the solution

(-2/x+4)=(4/x+3)

* i have been trying to figure these out all weekend and i can't. .

Q1. The answer is

Now, factorise the numerators and denominators:
x² - 16 = x² - 4² = (x + 4)(x - 4)
x² + 5x + 6 = x² + 2x + 3x + 2*3 = x(x+2) + 3(x+2) = (x + 2)(x + 3)
x² - 2x - 8 = x² + 2x - 4x - 2*4 = x(x+2) - 4(x+2) = (x + 2)(x - 4)
x² + 5x + 4 = x² + x + 4x + 4*1 = x(x+1) + 4(x+1) = (x + 1)(x + 4)


Now, cancel out some factors:


Q2. The answer is 
Since a² - b² = (a-b)(a+b), then a²- 64 = a² - 8² = (a-8)(a+8).



Q3. The answer is 


Now, cancel out some factors:




Q4. The answer is



Q5. The answer is x = 6






Let's check the solution:
Since:
Then: 
           
           
           
           
Thus, the solution is correct

Free points baby. free points baby. free points baby. hell yeah!