A Complex Simplification problem?

Question

y=(-1/(a+(x^2/a)))+3a/(x^2-a^2)

Answer 1

y = -1 / (a + x²/a) + 3a / (x² - a²)

Okay, start with the a + x²/a, get a common denominator of a, so you can add:
a² / a + x² / a = (a² + x²) / a

Now when you divide -1 by this, it's the same as multiplying by the reciprocal:
y = -1 * a / (a² + x²) + 3a / (a² - x²)
y = -a / (a² + x²) + 3a / (a² - x²)

Now you need to get the same denominator, so multiply the first by (a² - x²) and the second by (a² + x²)

y = [ -a(a² - x²) + 3a(a² + x²) ] / (a² - x²)(a² + x²)

Expand out the numerator:
y = [ -a^3 + ax² + 3a^3 + 3ax² ] / (a² - x²)(a² + x²)
y = ( 2a^3 - 4ax² ) / (a² - x²)(a² + x²)

Factor out a common 2a in the numerator:
y = 2a( a² - 2x² ) / (a² - x²)(a² + x²)

That's about as far as I can go...

Answer 2

puzzling,

y = -1 / (a + x²/a) + 3a / (x² - a²)

Okay, start with the a + x²/a, get a common denominator of a, so you can add:
a² / a + x² / a = (a² + x²) / a

Now when you divide -1 by this, it's the same as multiplying by the reciprocal:
y = -1 * a / (a² + x²) + 3a / (a² - x²))------------------> i think it should be
y = -1 *a/(a² + x²) + 3a/-(a²-x²)
you missed the -sign since you make (x²-a²) to (-)(a²-x²)