Simplify the function 𝑛 of 𝑥 equals 𝑥 plus seven divided by 𝑥 plus six plus 𝑥 divided by three 𝑥 and determine its domain.
In order to add fractions, they need to have equal bases; they need to be the same. So 𝑥 and three 𝑥, we can make this be the same by multiplying the first fraction by three. So now we can go ahead and distribute that three to the 𝑥 plus seven.
And now that we have a common denominator, we will keep that common denominator, and then we will combine like terms on the top. So first, we went ahead and just wrote them all on one line, and now let’s combine like terms.
So three 𝑥 plus 𝑥 is four 𝑥, and 21 plus six is 27 and then our common denominator of three 𝑥. So this will be our function simplified.
Now the domain is every number except what would make the denominator zero. So if we said three 𝑥 equal to zero and we divide both sides by three, 𝑥 is zero. Therefore, our function is equal to four 𝑥 plus 27 divided by three 𝑥, and the domain will be all real numbers minus zero.