Answer: -7x/10x^2 + 35.
Explanation: To simplify the expression (5/2x - 16/5) - (-35/3x1/7x21), we can follow these steps:
Step 1: Simplify the terms within the parentheses separately. - In the first set of parentheses, we have 5/2x and 16/5. Since the denominators are different, we need to find a common denominator. The least common multiple of 2 and 5 is 10. - Multiplying 5/2x by 5/5 (which is equivalent to 1) gives us 25/10x. - Multiplying 16/5 by 2/2 (also equivalent to 1) gives us 32/10. So, the first set of parentheses simplifies to (25/10x - 32/10).
Step 2: Simplify the second term, -35/3x1/7x21. - Here, we have a multiplication of three fractions: -35/3, 1/7, and 21. - We can multiply these fractions together in any order. To make it simpler, let's first multiply -35/3 by 1/7. This gives us -35/21. - Now, we can multiply -35/21 by 21. Cancelling out the common factor of 21, we are left with -35. So, the second term simplifies to -35. Step 3: Now that we have simplified both terms, we can subtract them. (25/10x - 32/10) - (-35) becomes 25/10x - 32/10 + 35.
Step 4: Find a common denominator for the two fractions, which is 10x.
- Multiplying 25/10x by x/x gives us 25x/10x^2. - Multiplying 32/10 by x/x also gives us 32x/10x^2.
So, the expression becomes (25x/10x^2 - 32x/10x^2) + 35.
Step 5: Combine the fractions by subtracting the numerators.
(25x - 32x)/10x^2 + 35.
Simplifying the numerator gives us -7x/10x^2 + 35.
Step 6: Finally, combine the terms into a single expression.
The simplified expression is -7x/10x^2 + 35.