Verified answer

I'm making assumptions about which parts are supposed to be fractions since you did not include parentheses or brackets.

3 - [(a - 4) / (a + 4)] = [(a² - 8) / (a + 4)]

The LCD is (a + 4). Multiply both sides by (a + 4) to get rid of the fractions.

(a + 4){3 - [(a - 4) / (a + 4)]} = (a + 4)[(a² - 8) / (a + 4)]

Distribute.

(a + 4)(3) + (a + 4)[-(a - 4) / (a + 4)]} = (a + 4)[(a² - 8) / (a + 4)]

3(a + 4) + (a + 4)[-(a - 4) / (a + 4)]} = (a + 4)[(a² - 8) / (a + 4)]

Cancel what you can.

3(a + 4) + (1)[-(a - 4) / (1)]} = (1)[(a² - 8) / (1)]

3(a + 4) - (a - 4) = a² - 8

Distribute.

3(a) + 3(4) - (a) - (-4) = a² - 8

3a + 12 - a + 4 = a² - 8

2a + 16 = a² - 8

Subtract 2a + 16 from both sides.

2a + 16 - 2a - 16 = a² - 8 - 2a - 16

0 = a² - 2a - 24

Factor.

0 = (a - 6)(a + 4)

Set each factor to 0 and solve.

a - 6 = 0

a = 6

a + 4 = 0

a = -4

But watch out! a = -4 is not a valid answer because it would result in denominators of 0.

Therefore:

a = 6

ANSWER: a = 6

(a+4) will cancel out from both sides...

so we r left with a-4=a^2-8 =>a^2-a-4=0 =>a=(1+√17)/2 and (1-√17)/2

I suggest you rewrite the expression correctly, using the appropriate parenthesis