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Please simplify the complex fraction correctly; x / x + 4/1 / x + 1 / x + 4
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Simplify the complex fraction x / x + 4/1 / x + 1 / x + 4
Answered by
GPT 3.5
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).
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).
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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).
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).
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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).
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).
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