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

Question

Accepted Answer

Hey everyone here we are asked to simplify the following expression where we have five minus five divided by Y all divided by five plus five divided by y. Now our first step here to simplify this expression is to work to combine our terms in the numerator and combine the terms in the denominator. So beginning with our numerator we see we need to find a common denominator, so so we can subtract the fraction from our whole number. So we take our whole number five and we multiply it by the value in the denominator of the other fraction. So we take five and multiply it by why divided by why? Because why divided by why is still just equal to one? So we are able to perform this operation without changing the expression. And now we just have five or sorry we have minus five divided by Y. And this is all divided by our denominator which undergoes a similar process. Here we take five and again multiply it by the denominator. So we again multiply five by Y divided by Y. But here we have plus five divided by Y. And now we just need to simplify our products. So beginning in our numerous we have five Y divided by y minus five divided by Y. And this is all divided by the denominator which simplifies to five, Y divided by Y plus five divided by Y. And now we can since we have found our common denominators, we can combine the terms in the numerator and the terms in the denominator. So doing this beginning with our numerator, we get five y minus five all divided by y. And this whole fraction is divided by five Y plus five all divided by Y. So now our next simplification we have to make is to take the reciprocal of our denominator and multiply it by the numerator because instead of dividing by a fraction we want to multiply by its reciprocal. So doing this, our expression becomes five y minus five, all divided by Y times the reciprocal which is why divided by five Y plus five. And now with this expression we see that we can make some cancelations. So we see we have a Y in the first denominator. And we also have a Y in the first numerator or in the second numerator. So both of these terms cancel. And now we can rewrite our expression with the terms we have low left. So we have five y minus five. All divided by five, Y plus five. So now looking at this expression, we see that in the numerator we can factor out a five from both terms. And we can also factor out a five from both terms in the denominator. So doing this in our numerator we have five times the quantity of y minus one, all divided by five times the quantity of Why plus one. And so now we see we have a five in the numerator and in the denominator. So both of these terms cancel. And so now our final simplified expression becomes why minus one? All divided by Y plus one. And this leaves us with our final answer, which is answer choice B. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

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

Key Concepts

Complex Fractions

Least Common Denominator (LCD)

Algebraic Simplification

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