Simplify each complex fraction. (2 - 2/y) / (2 + 2/y)

Question

Accepted Answer

Hey everyone here we are asked to simplify the following expression where we have three divided by X plus three all divided by three divided by x minus three. Now our first step here in simplifying this expression is to combine the terms in the numerator and combine the terms in the denominator. So beginning with our numerator we need to have our whole number here have the same denominator as our fraction. So with the numerator we have three divided by X plus three. So we take this whole number three and multiply it by X divided by X. And now in the denominator we repeat a similar process where we have three divided by x minus three. And now we need to multiply this minus three by the denominator which is X. So we have three times X divided by X. And now we just need to simplify our products. So in the numerator we have three divided by X plus three X divided by X. And this is all divided by the denominator where we will have three divided by x minus three X divided by X. And so now we see that we have our appropriate common denominators so we can go ahead and combine they're numerator. So beginning with the numerator of the whole expression we have three plus three X. Because we add together our enumerators here and this is all divided by X. And now this whole fraction is divided by the denominator which simplifies to three minus three X. All divided by X. And now our next simplification to make here is that we need to instead of dividing by this fraction in the denominator we need to multiply by its reciprocal. So rewriting our expression we have three plus three X. All divided by X times the reciprocal of the denominator which is X divided by three minus three X. And so now we can make some cancelations with what we have so far. So we see that we have an X in the denominator of our first fraction and we also have an X. In the numerator of our second fraction. So both of these X terms cancel. And so now we can rewrite our expression with what we have left and we have three plus three X. All divided by three minus three X. And so now in both the numerator and the denominator we see that we can factor out a common factor of three. So in our numerator we have three times the quantity of one plus x. And in our denominator we have three times the quantity of one minus X. And now we see we have a three in our numerator. And in our denominator so both of these terms cancel. And we are left with our final simplified expression where we have one plus X all divided by one minus X. And this is our final answer which is answer choice C Thanks for watching. I hope you found this video helpful and I'll see you again next time

Simplify each complex fraction. (2 - 2/y) / (2 + 2/y)

Key Concepts

Complex Fractions

Finding a Common Denominator

Simplifying Rational Expressions

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