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

Question

Accepted Answer

Hey everyone here we are asked to simplify the expression where we have five divided by a plus five plus five divided by a all divided by five divided by a. Now our first step here in simplifying this expression is to combine the terms in our numerator. So to combine the terms we need to find a common denominator between both both of these fractions. So that means we need to multiply the first fraction of five divided by a plus five by the value in the denominator of the second fraction. So we multiply the numerator and the denominator by A. And now with our second fraction we have plus five divided by A. But we need to multiply the fraction by the denominator of the first fraction. So we multiply the numerator and the denominator by a plus five. And now this whole expression is still divided by five divided by A. So now we just need to start simplifying our numerator here. So multiplying our terms together, we have five A divided by a times the quantity of a plus five and then we have plus five times the quantity of a plus five, all divided by a times X. Quantity of a plus five. And this whole expression is divided by five divided by a. So now that we have in our numerator we have common denominators between both of these fractions, we can add together their enumerators. So doing this we have five A plus and now factoring in this five, we have plus another five A plus 25 five all divided by eight times the quantity of a plus five and this is all divided by five divided by A. So now we just need to continue to simplify our numerator here by now adding together our like terms. So doing this, our numerator becomes 10 A plus all divided by A times the quantity of a plus five. And this is all divided by five divided by a. So now to continue to simplify our expression further we need to take our denominator and rather than dividing by this fraction in the denominator we want to multiply by its reciprocal. So doing this we can rewrite our expression as 10 a plus 25 all divided by a times the quantity of a plus five times the reciprocal of our denominator which is a divided by five. And now from here we can start making some more simplifications by canceling out terms that are in the numerator and the denominator. So here we can see that we have a in the first denominator and we also have a in the second numerator so they both cancel and now we are left with 10 A plus 25 all divided by five times the quantity of a plus five. And now our last simplification here we can factor out a five from both terms in our numerator and that gives us five times the quantity of two a plus five, all divided by five times the quantity of a plus five. And now here we see, we have A for five in our numerator and we also have a five in the denominator, so both of these terms cancel. And this leaves us with our final simplified expression where we have the quantity of two A plus five divided by the quantity of a plus five. And this is our answer here for answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

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

Key Concepts

Complex Fractions

Common Denominator

Algebraic Manipulation

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