3/4(4/3х-4)-8(2 1/4х+3/8)

To simplify the expression, let's start by simplifying each term separately.

Starting with the first term: 3/4(4/3х - 4) To simplify this term, we'll multiply 3/4 by both terms inside the parentheses: (3/4 * 4/3х) - (3/4 * 4)

The 3's in the numerator and denominator cancel out, as well as the 4's, leaving us with: х - 3

Moving on to the second term: -8(2 1/4х + 3/8) Notice that 2 1/4 can be converted to an improper fraction: 2 1/4 = (8/4 + 1/4) = 9/4

Now, we'll multiply -8 by both terms inside the parentheses: -8 * (9/4х + 3/8)

Distributing the multiplication, we get: (-8 * 9/4х) - (8 * 3/8)

Simplifying further, we have: -72/4х - 24/8

Next, we need to find a common denominator for the fractions so that we can combine them: -72/4х - 24/8 = -72/4х - 3/2

Now, we can combine the two terms to get the final answer: (х - 3) - (72/4х + 3/2)

To simplify the expression further, we can combine like terms: х - 3 - 72/4х - 3/2

Multiply the second term by 2/2 to get a common denominator: х - 3 - 144/8х - 3/2

Now, we can find a common denominator for all the terms: 8х - 24 - 144х/8 - 12/2

Simplifying further, we have: 8х - 24 - 18х - 12

Combining like terms, we get: -10х - 36

Therefore, the simplified expression is -10х - 36.