Please simplify the complex fraction correctly; x / x + 4/1 / x + 1 / x + 4

Answer 1

To simplify the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)), we can follow these steps:

1. Combine the fractions in the numerator and the denominator separately:
- In the numerator: x
- In the denominator: (x + 4) / (1 / (x + 1) / (x + 4))

2. To simplify the denominator further, divide the denominator into two separate fractions:
- (x + 4) / ((1 / (x + 1)) / (x + 4))
=> (x + 4) / (1 / (x + 1) * (x + 4))
=> (x + 4) / (x + 4) * (x + 1)
=> (x + 4) / (x + 1)

Therefore, the simplified form of the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) is just x / (x + 1).

Answer 2

Are you 100% sure?

Answer 3

I apologize for the mistake in my previous response. Let's simplify the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) correctly:

x / (x + 4) / (1 / (x + 1) / (x + 4))

= x / (x + 4) * ((x + 4) / (1 / (x + 1)))

= x / (x + 4) * (x + 4) * (x + 1)

= x / (x + 4) * (x^2 + 5x + 4)

= x / x^2 + 5x + 4

Therefore, the simplified form of the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) is x / x^2 + 5x + 4.

Answer 4

Are you sure?

Answer 5

I apologize for the mistake in my previous responses. Let's simplify the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) correctly:

To simplify the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)), follow these steps:

1. Flip the second fraction and multiply:
x / (x + 4) * (x + 4) / (1 / (x + 1))

2. Rewrite the denominator as a multiplication:
x / (x + 4) * (x + 4) / 1 * (x + 1)

3. Simplify:
x / (x + 4) * (x + 1)

4. Further simplify by expanding:
= x(x + 1) / (x + 4)
= x^2 + x / (x + 4)

Therefore, the simplified form of the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) is (x^2 + x) / (x + 4).

Answer 6

Are you sure about your response?

Answer 7

My previous responses contained errors. Let's simplify the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) correctly:

Given complex fraction: x / (x + 4) / (1 / (x + 1) / (x + 4))

Take the reciprocal of the denominator of the main fraction:
= x / (x + 4) * (x + 4) / 1 / (x + 1)
= x / (x + 4) * (x + 4) * (x + 1)

Simplify by expanding and canceling out terms:
= x(x + 1) / 1
= x^2 + x

Therefore, the simplified form of the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) is x^2 + x.

Answer 8

Simplify the complex fraction x / x + 4/1 / x + 1 / x + 4

Answer 9

To simplify the complex fraction x / (x + 4)/(1 / (x + 1) / (x + 4)), we can follow these steps:

1. First, simplify the expressions in the numerator:
x / (x + 4) = x / (x + 4)

2. Simplify the denominator by taking the reciprocal of the fraction and multiplying it:
(1 / (x + 1)) / (x + 4) = 1 / (x + 1) * 1 / (x + 4) = 1 / ((x + 1) * (x + 4)) = 1 / (x^2 + 5x + 4)

3. Now simplify the main fraction:
x / (x + 4) / (1 / (x + 1) / (x + 4)) = x / (x + 4) * (x^2 + 5x + 4) = x(x^2 + 5x + 4) / (x + 4) = x^3 + 5x^2 + 4x / (x + 4)

Therefore, the simplified form of the complex fraction x / (x + 4) / (1 / (x + 1) / (x + 4)) is x^3 + 5x^2 + 4x / (x + 4).