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

To simplify the expression 4 7/32x - (3 3/4x - 1 7/32x), you need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

Let's simplify step by step:

1. Convert the mixed numbers to improper fractions so it's easier to work with:

• 4 7/32 = (4 * 32/32) + (7/32) = (128/32) + (7/32) = 135/32
• 3 3/4 = (3 * 4/4) + (3/4) = (12/4) + (3/4) = (12/4) + (3/4) = (15/4)
• 1 7/32 = (1 * 32/32) + (7/32) = (32/32) + (7/32) = 39/32

Now the expression can be written as: 135/32x - (15/4x - 39/32x)

2. Simplify the expressions within the parentheses first: To subtract 15/4x and 39/32x, you need to find a common denominator. The common denominator of 4 and 32 is 32.

• The fraction 15/4 needs to be converted to have this common denominator, which would be 15/4 * 8/8 = 120/32.

The expression in the parentheses is now: 120/32x - 39/32x

Subtract the fractions by subtracting their numerators: 120/32x - 39/32x = (120 - 39)/32x = 81/32x

3. The parentheses simply indicate a grouping and not multiplication by a negative, so now we have: 135/32x - 81/32x

4. Now subtract the non-parenthesised term from the result of the simplified parentheses: 135/32x - 81/32x = (135 - 81)/32x = 54/32x

5. If you want, you can simplify the fraction: 54/32 can be simplified by dividing both the numerator and the denominator by their greatest common divisor which is 2: 54/32 = 27/16 when simplified.

Therefore, the simplified expression is: 27/16x

And that's the simplified form of the original expression.