Solve.

See how this puppy works out for ya'll:

(-3a)/(a+12) = (6)/(a-13)

We know that the demoninator cannot be zero because you cannot divide by zero, therefore, a cannot be -12 (because -12+12=0) and a cannot be 13 (because 13-13=0).

Go from there...

The common denominator is (a+12)(a-13). After cross multiplying, you'll get:

-3a(a-13) = 6(a+12)

No more fractions. YAY! Now, distribute:

-3a^2+39 = 6a+72

Now, set your equation to zero, which means to subtract 6a from both sides and subtract 72 from both sides. You'll get:

-3a^2-6a-33=0

We have a greatest common factor that needs to come out. We do this to set our variable to a single, squared variable. This problem looks like this now:

-3(a^2+2a+11)=)

Now we're going to factor this trinomial. Take 11 and find the factor (number multiplied together) to get 11 that when added equal to 2. There are only two numbers that can be multiplied to get 11, 11*1=11 or -11*-1=+11. But neither equal 2. 11+1=12 and -11-1=-12

What do I do now? I'll ask the teacher Monday because, um, I'm stuck! The answers are (a= 3, 8), but how if it cannot be factored? Complete the square? But that wouldn't give you a perfect square. Argh! >:(