Rational numbers and expressions math problem..?

Question

simplify and show all work please:

1) 9/x-3 - x^2/-3+x

Answer 1

(x^2 +2x- 30) / (x^2-9)

Answer 2

(9/[x - 3]) - (x²/[- 3 + x]) = 0

9 - x² = 0

x² = 9

x = +/- 3

Answer: x = 3, - 3; Factors: (x + 3)(x - 3)

Proof (x = 3):

9/(3 - 3) = 3²/(- 3 + 3)

9/0 = 9/0

0 = 0

Proof (x = - 3):

9/(- 3 - 3) = - 3²/(- 3 - 3)

9/- 6 = 9/- 6

- 3/2 = - 3/2

Answer 3

9/(x - 3) - x^2/(-3 +x)

or

9/(x - 3) - x^2/(x - 3)

Add the fractions to get

(9 - x^2)/(x - 3)

Factor the numerator using the difference of squares method...

(3 - x)(3+x)/(x - 3)

Note that (3 - x) = -1(x - 3)

so...

-1(x - 3)(x + 3) / (x - 3)

Now cancel the (x - 3) factor

-1(x + 3)

Remember that when solving you keep the original restrictions, so....

-1(x+3) where x != 3

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Note that x can't be 3 because in the original equation you would get...

9/0 - 9/0 and you can't divide by 0 (9/0 is undefined)