(1+1/x)/(1-1/x)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (1 + 1/x) / (1 - 1/x)

This expression can be simplified using a few algebraic steps. Here's how:

1. Find a common denominator for the numerator and denominator:

• For the numerator (1 + 1/x), the common denominator is x. So, we rewrite it as (x/x + 1/x) = (x+1)/x.
• Similarly, for the denominator (1 - 1/x), the common denominator is x. We rewrite it as (x/x - 1/x) = (x-1)/x.

2. Rewrite the expression with the simplified fractions:

Now the expression becomes: [(x+1)/x] / [(x-1)/x]

3. Dividing fractions:

Dividing by a fraction is the same as multiplying by its inverse. Therefore:

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

4. Simplify by canceling out common factors:

Notice that 'x' appears in both the numerator and denominator. We can cancel these out, leaving:

(x+1)/(x-1)

Therefore, the simplified form of the expression (1 + 1/x) / (1 - 1/x) is (x+1)/(x-1).

Important Note: This simplification holds true as long as x is not equal to 0 or 1. If x = 0, the original expression would be undefined due to division by zero. If x = 1, the denominator (x - 1) would equal zero, resulting in an undefined expression.