Question

(a/a-3 + 3-a/a+3) * (a+3/1-a)

Answer 1

A/a=1
(1-3+3-1+3)=3
(a+3/1-a)=(a-a+3)=3
3*3=9

Answer 2

To simplify the expression, let's break it down step by step:

Given expression:

[(a/(a-3)) + (3-a)/(a+3)] * [(a+3)/(1-a)]

Step 1: Simplify the fractions within the brackets.

[(a/(a-3)) + (3-a)/(a+3)] can be rewritten as [(a*(a+3) + (3-a)(a-3))/((a-3)(a+3))].

Step 2: Simplify the second fraction [(a+3)/(1-a)].

The denominator of the second fraction becomes (1 - a) when simplified.

Step 3: Combine the fractions.

[(a*(a+3) + (3-a)(a-3))/((a-3)(a+3))] * [(a+3)/(1-a)]

Step 4: Simplify further.

Expanding the numerator in the first fraction, we have:

[(a^2 + 3a + 3a - 9 - a^2 + 3a - 9) / ((a-3)*(a+3))] * [(a+3)/(1-a)]

Combining like terms, we get:

[(6a - 15) / ((a-3)*(a+3))] * [(a+3)/(1-a)]

Step 5: Simplify the expression.

[(6a - 15) * (a+3)] / [(a-3)(a+3)(1-a)]

The (a+3) terms cancel out:

[(6a - 15) / ((a-3)*(1-a))]

The final simplified expression is:

(6a - 15) / ((a-3)*(1-a))