Question

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

Answer 1

   $\frac{x+3}{x^2+3}*(\frac{x+3}{x-3}-\frac{x-3}{x+3} )=$

$=\frac{x+3}{x^2+3}*\frac{(x+3)*(x+3)-(x-3)*(x-3)}{(x-3)*(x+3)}=$

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

$=\frac{(x+3)*12x}{(x^2+3)(x-3)(x+3)}=$

$=\frac{12x}{(x^2+3)(x-3)}$

Answer 2

(x+3)/(x²+3)*((x+3)/(x-3)-(x-3)/(x+3))=

((х+3)*(х²+9+6х-х²+6х-9)/((х²+3)*(х+3)(х-3))=

12х/((х-3)(х²+3))

Answer 3

To simplify the given expression:

First, let's simplify the numerator of the first fraction:

(x + 3) * (x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9

Now, let's simplify the denominator of the first fraction:

(x^2 + 3)

The first fraction simplifies to:

(x + 3) / (x^2 + 3) = (x + 3) / (x^2 + 3)

Now, let's simplify the numerator of the second fraction:

(x + 3) * (x - 3) = x^2 - 3x + 3x - 9 = x^2 - 9

Let's simplify the denominator of the second fraction:

(x - 3) * (x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9

The second fraction simplifies to:

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

Now, let's substitute the simplified fractions back into the expression:

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

= ((x + 3) / (x^2 + 3)) * ((x + 3 - (x - 3)) / (x + 3))

= ((x + 3) / (x^2 + 3)) * (x + 3 - x + 3) / (x + 3))

= ((x + 3) / (x^2 + 3)) * (6 / (x + 3))

Now, we can cancel out (x + 3) terms in the numerator and denominator:

= 6 / (x^2 + 3)

Therefore, the simplified expression is 6 / (x^2 + 3).