How to Simplify f(x)/g(x) with Common Denominators

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In summary, when we say "simplify f(x)/g(x)", we are asking to express the function f(x) divided by g(x) in its most simplified form. This involves factoring both the numerator and denominator, canceling out any common factors, and reducing the fraction to its lowest terms if possible. This can be done even if there are variables in both the numerator and denominator, but if there are no common factors, the fraction cannot be simplified any further. Simplifying f(x)/g(x) is important for better understanding and working with the function, identifying key characteristics, and determining the domain and range of the function.
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miket9
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"simplify the expression"
need answer in the following:
f(x)/g(x)
 

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I think you mean (just saying "f(x)/g(x)" is very vague) that you want to make a single fraction of 3- 4/(x-2). Change to "common denominators" which here is the only denominator, x- 2, and subtract: 3(x-2)/(x-2)- 4/(x-2)= (3x-2- 4)/(x-2)= (3x- 6)/(x-2).
 

FAQ: How to Simplify f(x)/g(x) with Common Denominators

What does "Simplify f(x)/g(x)" mean?

When we say "simplify f(x)/g(x)", we are asking to express the function f(x) divided by g(x) in its most simplified form. This means reducing the fraction as much as possible and canceling out any common factors between the numerator and denominator.

How do I simplify f(x)/g(x)?

To simplify f(x)/g(x), you can follow a few steps:

  1. Factor both the numerator and denominator of the fraction.
  2. Cancel out any common factors between the numerator and denominator.
  3. If possible, reduce the fraction to its lowest terms.

Can I simplify f(x)/g(x) if there are variables in both the numerator and denominator?

Yes, you can still simplify f(x)/g(x) even if there are variables in both the numerator and denominator. You would follow the same steps as mentioned before, but make sure to factor out any common variables before canceling them out.

What if there are no common factors between the numerator and denominator?

If there are no common factors between the numerator and denominator, the fraction cannot be simplified any further. In this case, the fraction is already in its simplest form and cannot be simplified any more.

Why is it important to simplify f(x)/g(x)?

Simplifying f(x)/g(x) can make it easier to understand and work with the function. It also helps to identify any important characteristics of the function, such as asymptotes or points of discontinuity. Additionally, simplifying can also help in finding the domain and range of the function.

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