(1/sqrt(1-(3x/4)^2) * 3/4

To simplify the expression (1/sqrt(1-(3x/4)^2)) * (3/4), we can follow these steps:

Step 1: Simplify the expression inside the square root:

The square of (3x/4) can be written as (3x/4)^2 = (9x^2/16).

So, the expression becomes (1/sqrt(1-(9x^2/16)) * (3/4).

Step 2: Simplify the denominator under the square root:

To simplify 1 - (9x^2/16), we can find a common denominator, which is 16. The expression becomes (16/16) - (9x^2/16), giving us (16 - 9x^2)/16.

So, the expression becomes (1/sqrt((16-9x^2)/16)) * (3/4).

Step 3: Simplify the square root:

To simplify the square root, we divide the numerator and denominator of the expression by the square root of 16, which is 4.

The expression becomes (1/(sqrt((16-9x^2)/16) * (3/4)) * (4/4).

Simplifying further, (1/(sqrt(16-9x^2)/4)) * (3/4).

Step 4: Combine the fractions:

To combine the fractions, multiply the numerators together and multiply the denominators together.

The expression becomes (3/(4 * sqrt(16-9x^2)) * (1/4).

Finally simplifying, the expression (3/16) * (1/sqrt(16-9x^2)), which can be written as (3/(16 * sqrt(16-9x^2))).