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

To simplify the equation 4 7/32x - (3 3/4x - 1 7/32x), you will need to perform several steps including distributing the negative sign through the parentheses and combining like terms. Here's how you do it step by step:

First, convert the mixed fractions to improper fractions to make calculations easier.

1. Convert 4 7/32x

• This is equal to ((4 * 32) + 7)/32 x which simplifies to 135/32 x

2. Convert 3 3/4x

• This is equal to ((3 * 4) + 3)/4 x which simplifies to 15/4 x

3. Convert 1 7/32x

• This is equal to ((1 * 32) + 7)/32 x which simplifies to 39/32 x

Now let's do the calculations with the improper fractions:

4 7/32x - (3 3/4x - 1 7/32x) is now:

135/32x - (15/4x - 39/32x)

Next, distribute the negative sign into the parentheses:

135/32x - 15/4x + 39/32x

To subtract 15/4x from 135/32x, you need to have a common denominator. The least common denominator for 32 and 4 is 32.

Convert 15/4x to equivalent fraction with a denominator of 32:

15/4x = (15 * 8)/(4 * 8)x = 120/32x

Now the expression looks like this:

135/32x - 120/32x + 39/32x

Now you can combine like terms:

(135 - 120 + 39)/32x = 54/32x

Finally, simplify the fraction 54/32 by dividing both the numerator and the denominator by their greatest common divisor which is 2:

54/32 = (54 ÷ 2)/(32 ÷ 2) = 27/16x

Therefore, the simplified expression is:

27/16x