Simplify each complex fraction. [ 1 + 1/(1-b) ] / [ 1 - 1/(1+b) ]

Question

Accepted Answer

Hey everyone here we are asked to simplify the following expression where we have two minus one divided by the quantity of two plus C. This is all divided by two plus one divided by the quantity of two minus C. And so now our first step here in simplifying our expression is to combine the terms in the numerator and combine the terms in the denominator. So beginning in the numerator we need to get the whole number two to have a common denominator with the other fraction. So we need to multiply two by the quantity of two plus C divided by two plus C. And then we are subtracting our fraction here of one divided by two plus C. And this is all divided by our denominator where we need to repeat a similar process. But instead we are taking the whole number which is again two and we're multiplying it by the quantity of two minus C, divided by two minus C. And then we add the other fraction which is one divided by two minus C. So now we just need to start simplifying our products here. So factoring in our, sorry multiplying these terms together, starting with our numerator, we have two times the quantity of two plus C. All divided by two plus C. Then we subtract the other fraction which is one divided by two plus C. And this is all divided by our denominator which we can begin to simplify as two times the quantity of two minus C. All divided by two minus C. And then we add the other fraction which is one divided by two minus C. And now we just need to continue to simplify what we have here by first factoring in both of the twos from the expression that we have. So doing this beginning in the numerator we have four plus two c minus one. All divided by two plus C. And now in the denominator we have four minus two C. Plus one. All divided by two minus C. And so now we just need to combine our like terms. So again beginning in our numerator we have four minus one which gives us three plus two C. All divided by two plus C. And this is all divided by our denominator which simplifies to five minus two C. All divided by two minus C. And now we can simplify our expression further by instead of dividing by this second fraction here we can multiply by its reciprocal. So doing this we can rewrite our expression as three plus two C. All divided by two plus C. Times the reciprocal of this second fraction which is two minus C. All divided by five minus two C. And so now we just need to combine our terms our fractions here by multiplying the enumerators together and multiplying the denominators together. So doing this we just have in the numerator we have the quantity of three plus two C. Times the quantity of two minus C. All divided by the quantity of two plus C times the quantity of five minus two C. And with this we have found our fully simplified expression, and so we are left with answer choice D. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Simplify each complex fraction. [ 1 + 1/(1-b) ] / [ 1 - 1/(1+b) ]

Key Concepts

Complex Fractions

Common Denominator

Algebraic Manipulation

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