Question

Simplify (5/2x -16/5)-(-35/3x1/7x21)​

Answer 1

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.

Answer 2

Before we can simplify this expression, we need to first find a common denominator for all the fractions. The prime factorization of the denominators is:

2 × 5

3 × 7 × x

Therefore, a common denominator is:

2 × 5 × 3 × 7 × x = 210x

Using this common denominator, we can rewrite the expression as:

[(5 × 21) / (2 × 5 × x) - (16 × 42) / (5 × 2 × 21 × x)] - [(-35) / (3 × x × 7 × 21)]

Simplifying each fraction, we get:

[105 / (10x) - 672 / (210x)] - [-5 / (3 × 7 × x × 21)]

Combining the two fractions and simplifying, we get:

[105 - 672] / (10x) + [5 / (3 × 7 × x × 21)]

= -567 / (10x) + 1 / (3 × 7 × x)

= (-567 × 21 + 10) / (210x)

= -11897 / (210x)

Therefore, the simplified expression is:

-11897 / (210x)