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remorris
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I know that (1-x)/(1+x) is equivalent to (2/(x+1)) - 1 via 'hand waving' in my textbook but i cannot figure out the steps to arrive at this result. Suggestions??
remorris said:I know that (1-x)/(1+x) is equivalent to (2/(x+1)) - 1 via 'hand waving' in my textbook but i cannot figure out the steps to arrive at this result. Suggestions??
mfb said:You can write 1-x as -x-1+2=-(x+1)+2 and simplify.
That is a usual trick for fractions like yours.
remorris said:I know that (1-x)/(1+x) is equivalent to (2/(x+1)) - 1 via 'hand waving' in my textbook but i cannot figure out the steps to arrive at this result. Suggestions??
The general formula for simplifying (1+x)/(1-x) is (1+x)*(1+x) / (1-x)*(1+x). This can be further simplified to (1+x)^2 / (1-x^2).
The main principle behind simplifying (1+x)/(1-x) is to eliminate the fraction by multiplying both the numerator and denominator by the same expression. This will result in a simpler expression without any fractions.
Yes, (1+x)/(1-x) can be simplified further by using algebraic identities such as (a+b)(a-b) = a^2 - b^2. This will result in the simplified form of 1 + 2x / (1-x^2).
Simplifying (1+x)/(1-x) can help in solving equations and simplifying mathematical expressions. It can also help in understanding the relationship between the numerator and denominator in a fraction.
Yes, there are restrictions on the values of x in simplifying (1+x)/(1-x). x cannot be equal to 1 or -1 as it will result in an undefined expression. Additionally, x cannot be equal to any value that would result in the denominator being equal to 0.