Question

Can someone help me express as a single fraction
\[\frac{ 1 }{ x+1 }+\frac{ 1 }{ x }\] ?

Answer 1

How you can have them as a single fraction is when the denominators are the same, right? And how do you do that?

Answer 2

by adding + 1 to the 1 and the x

Answer 3

How can you just add something to the denominator though? Here's a hint: Find a common multiple of x+1 and x

Answer 4

the common multiple is x

Answer 5

so would the single fraction be x

Answer 6

When you are given an expression like x+1, you have to treat it like a single term. So x+1 is one thing and x is one thing like numbers 3 and 5. How would you find the common multiple of 3 and 5?

Answer 7

they do not have a common multiple

Answer 8

Of course they do! Haha. Don't you multiply them together and you end up with one? I think you were thinking of common factor. If so then no, they don't have any.

Answer 9

So back to my question what would the single fraction be???????/

Answer 10

Hey there farm girl :)

So our `common denominator` would be the product of the two denominators.\[\Large \cfrac{1}{x+1}+\cfrac{1}{x}\quad=\quad \cfrac{\color{teal}{(x)}1}{\color{teal}{(x)}(x+1)}+\cfrac{1\color{orangered}{(x+1)}}{(x)\color{orangered}{(x+1)}}\]

Answer 11

See how they both have the same denominator now?
(x)(x+1)

Answer 12

We had to multiply the first fraction by x/x in order to achieve this, and also we had to multiply the second fraction by (x+1)/(x+1).

Answer 13

Now that they have the same denominator, we can write the expression as a single fraction:\[\Large \frac{\color{teal}{x}+\color{orangered}{(x+1)}}{(x)(x+1)}\]Which can be simplified a bit further :)