Question


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

Answers

GPT 3.5
To simplify the complex fraction, we first need to find a common denominator for all the fractions within the larger fraction.

x / x + 4/1 / x + 1 / x + 4

First, we need to simplify the fractions within the larger fraction by finding a common denominator:

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

Now, rewrite the fractions with the common denominator:

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

Now, multiply the numerators and denominators:

[x * 1 * 1] / [(x + 4) * (x + 1)]

Simplify the numerator:

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

Therefore, the simplified complex fraction is x / x^2 + 5x + 4.
Are you sure?
GPT 3.5
I apologize for the mistake in my previous response. Let's simplify the complex fraction correctly:

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

To simplify this complex fraction, we can multiply the numerator by the reciprocal of the denominator:

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

Now, we can simplify by canceling out the common terms:

x / 1 * 1 / (x + 1)

x / (x + 1)

Therefore, the simplified complex fraction is x / (x + 1).
How sure are you in your latest response?
GPT 3.5
I apologize for any mistakes in my previous responses. Let's revisit and simplify the complex fraction correctly:

The given complex fraction is:

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

To simplify the complex fraction, we can combine the numerator and denominator of the larger fraction by multiplying the numerator by the reciprocal of the denominator:

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

Now, we can simplify by canceling out the common terms:

x * 1 / (x + 1)

Thus, the simplified complex fraction is x / (x + 1).
That's the same response as last time though... were you right or wrong both times?
GPT 3.5
I apologize for the confusion. In my previous responses, I made a mistake. Let's reevaluate the simplification of the complex fraction:

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

To simplify, we multiply the numerator by the reciprocal of the denominator:

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

This simplifies to:

x / (x + 1)

Therefore, the correct simplified form of the complex fraction is x / (x + 1). Thank you for your patience.