To solve the first equation, let's simplify it step by step:

√x^2 - 9 - 3√x - 3 = 0

First, let's simplify the square root:

x - 9 - 3√x - 3 = 0

Next, let's combine like terms:

x - 12 - 3√x = 0

Now, let's isolate the square root term:

-3√x = -x + 12

Divide both sides by -3:

√x = (x - 12)/3

Now, square both sides to eliminate the square root:

x = (x - 12)^2/9

Expand the numerator:

x = (x^2 - 24x + 144)/9

Multiply both sides by 9 to eliminate the fraction:

9x = x^2 - 24x + 144

Rearrange the equation:

x^2 - 33x + 144 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. However, in this case, the equation can be factored:

(x - 9)(x - 16) = 0

Setting each factor equal to zero:

x - 9 = 0 or x - 16 = 0

Solving for x:

x = 9 or x = 16

Therefore, the solutions to the first equation are x = 9 and x = 16.

To solve the second equation, let's simplify it step by step:

√(4x + 3)/(x + 1) = 3

First, let's square both sides to eliminate the square root:

(4x + 3)/(x + 1) = 3^2

Simplifying:

(4x + 3)/(x + 1) = 9

Now, let's cross-multiply:

9(x + 1) = 4x + 3

Distribute:

9x + 9 = 4x + 3

Subtract 4x from both sides:

5x + 9 = 3

Subtract 9 from both sides:

5x = -6

Divide both sides by 5:

x = -6/5

Therefore, the solution to the second equation is x = -6/5.