Simplify each complex fraction. See Examples 5 and 6. (1 + 1/x...

Question

Simplify each complex fraction. See Examples 5 and 6. (1 + 1/x) / (1 − 1/x)

Accepted Answer

Hello, everyone. We are asked to simplify the following rational expression. Five plus five divided by a divided by five minus five, divided by a, our answer choices are a, the parentheses A plus one divided by the parentheses. A minus one. B, the parentheses A minus one divided by the parentheses. A plus one, C one divided by the parentheses. A plus one, D one divided by the parentheses. A minus one. So starting out again, I have five plus five divided by A as a numerator and then five minus five divided by A, as a denominator. I'm going to take my numerator and try to make a common denominator which would be A. So I'm gonna multiply five by a over A or a divided by A. She'll give me five a divided by A plus five divided by A and I'm gonna do the same in my denominator. So I need to have a denominator for these two fractions of a. So multiplying five by a divided by A will give me five, a divided by a minus five divided by A. I'm gonna write these as a single fraction. So my numerator would be five A plus five divided by a divided by the denominator, which would be five A minus five divided by A. Now I'm gonna rewrite this so that I have it as um two fractions with a division sign in between them. So five, a plus five divided by a divided by five, a minus five divided by A. And I recall that when I divide fractions, I multiply by the reciprocal. So my first fraction does not change, it says five A plus five divided by A and then we multiply by the reciprocal of the second fraction, which would be a divided by five A minus five. I'm gonna cross reduce my A's and that would give me five A plus five divided by five A minus five. So I'm not done quite yet because I noticed that there is a GCF in both the numerator and the denominator here. So in my numerator, I can factor a five out and I'll have five multiplied by the parentheses. A plus one. And then the denominator, I can also factor out of five. So I have five multiplied by the parentheses. A minus one. And now looking at this, I can cancel those fives and I am left with a plus one divided by a minus one. And because I can't cancel parts of addition or subtraction sentences, this is my answer. So a plus one divided by a minus one which is answer choice. A have a nice day.

Simplify each complex fraction. See Examples 5 and 6. (1 + 1/x) / (1 − 1/x)

Key Concepts

Complex Fractions

Algebraic Manipulation

Reciprocal and Division of Fractions

Watch next