4 7/32x-(3 3/4x - 1 7/32x)

Let's simplify the expression step by step:

4 7/32x - (3 3/4x - 1 7/32x)

First, we can convert the mixed numbers to improper fractions to make the calculation easier:

3 3/4x can be converted as follows: 3 3/4 = 3 + 3/4 = (3 * 4)/4 + 3/4 = 12/4 + 3/4 = 15/4 So, 3 3/4x = (15/4)x

1 7/32x is already an improper fraction, so we can leave it as is.

Now the expression looks like this:

4 7/32x - ((15/4)x - 1 7/32x)

Next, distribute the negative sign inside the parentheses:

4 7/32x - (15/4)x + 1 7/32x

Now, combine like terms. To do this, we need to make sure all the terms have the same denominator. The least common denominator for 32 and 4 is 32.

(15/4)x can be converted to an equivalent fraction with a denominator of 32 as follows: (15/4) * (8/8) = (158)/(48) = 120/32

Now, rewrite the expression with the common denominator (32):

4 7/32x - 120/32x + 1 7/32x

Combine the like terms:

(432/32 + 7/32 - 120/32 + 132/32 + 7/32)x (128/32 + 7/32 - 120/32 + 32/32 + 7/32)x (135/32 - 120/32 + 39/32)x (15/32 + 39/32)x (54/32)x

Now, simplify the common factor in the resulting fraction if possible:

54/32 cannot be simplified since 54 and 32 do not have common factors (other than 2, but 54 is not divisible by 16 to reduce completely).

So, the simplified expression is:

(54/32)x (or 1 22/32 x when expressed as a mixed number, which also simplifies to 1 11/16 x)

Final result: (54/32)x or 1 11/16 x