Fraction Simplification: (1-(y2/x2))/(1+(y2/x2))

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In summary, fraction simplification is the process of reducing a fraction to its simplest form. It is important because it makes fractions easier to work with and understand. The steps to simplify a fraction involve finding the greatest common factor and dividing both the numerator and denominator by it. All fractions can be simplified, but some may already be in their simplest form. Simplifying and reducing a fraction refer to the same process.
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Homework Statement


hey guys just wondering if anyone could help me simplify this. thansk

[1-(y2/x2)]/[1+(y2/x2)]

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The Attempt at a Solution

 
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To simplify this fraction, we can start by factoring out the common factor of y^2/x^2 in both the numerator and denominator:

[1-(y2/x2)]/[1+(y2/x2)] = [(1-y2/x2)]/[(1+y2/x2)]

Next, we can use the identity (a-b)(a+b) = a^2 - b^2 to simplify the numerator:

[(1-y2/x2)] = [1-y2/x2] * [1+y2/x2] = 1^2 - (y2/x2)^2 = 1 - y^2/x^2

Similarly, we can use the same identity to simplify the denominator:

[(1+y2/x2)] = [1+y2/x2] * [1-y2/x2] = 1^2 - (y2/x2)^2 = 1 - y^2/x^2

Substituting these simplified expressions back into our original fraction, we get:

[1-(y2/x2)]/[1+(y2/x2)] = [(1-y^2/x^2)]/[(1-y^2/x^2)] = 1

Therefore, the simplified fraction is equal to 1.
 

What is fraction simplification?

Fraction simplification is the process of reducing a fraction to its simplest form. This means finding the equivalent fraction with the smallest possible numerator and denominator.

Why is it important to simplify fractions?

Simplifying fractions makes them easier to work with in calculations and comparisons. It also helps to visually understand the relationship between different fractions.

What are the steps to simplify a fraction?

The steps to simplify a fraction are: 1) Find the greatest common factor (GCF) of the numerator and denominator. 2) Divide both the numerator and denominator by the GCF. 3) Repeat this process until the GCF is 1 or the fraction cannot be simplified any further.

Can all fractions be simplified?

Yes, all fractions can be simplified. However, some fractions may already be in their simplest form, so no further simplification is needed.

What is the difference between simplifying and reducing a fraction?

Reducing a fraction and simplifying a fraction refer to the same process of finding the simplest form of a fraction. Some people may use the term "reducing" when the numerator and denominator are divided by their greatest common factor (GCF), while others may use "simplifying".

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