Question

Expand [x+2/x-3] [x-2/x-3]

Answer 1

`= \frac{ {x}^(2) - 4 }{ {x }^(2)-6x+9 } \\`

Explanation:

`(x + 2)/(x - 3) * (x - 2)/(x - 3) \\ ((x + 2)(x - 2))/((x - 3)(x - 3)) \\ \frac{x(x - 2) + 2(x - 2)}{ {(x - 3)}^(2) } \\ \frac{ {x}^(2) - 2x + 2x - 4 }{ {x}^(2) - 6x+9} \\ = \frac{ {x}^(2) - 4 }{ {x }^(2) -6x+9 }`

Answer 2

`(x^2-4)/(x^2-6x+9)`

Explanation:

We assume you want to expand ...

`(x+2)/(x-3)\cdot(x-2)/(x-3)=((x+2)(x-2))/((x-3)^2)=\boxed{(x^2-4)/(x^2-6x+9)}`

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In each case, the product of the factors is ...

(x +a)(x +b) = x² +(a+b)x +ab

For the numerator, you have (a, b) = (2, -2).

For the denominator, you have (a, b) = (-3, -3).