Question

Simplify an expression

Answer 1

`(20+2k)/(3k+12)`

Explanation:

Since there is no equals sign here, we are not solving this. The only way to simplify is to get a common denominator and write the expression as a single expression. We can begin by noting that the second term has a k in the numerator and in the denominator, and those cancel each other out. That is the first simplification we can perform. That leaves us with:

`(4)/(k+4)+(2)/(3)`

In the first term, the denominator is k + 4, in the second term it is just 3. Therefore, the common denominator is 3(k+4). We are missing the 3 in the denominator of the first term, so we will multiply in 3/3 by that term. We are missing a (k + 4) in the second term, so we will multiply in (k + 4)/(k + 4) by that term:

`((3)/(3))((4)/(k+4))+((k+4)/(k+4))((2)/(3))`

Multiplying fractions requires that I multiply straight across the top and straight across the bottom. That gives me:

`(12)/(3k+12)+(2k+8)/(3k+12)`

Now that the denominators are the same, I can put everything on top of that single denominator:

`(12+2k+8)/(3k+12)`

Th final simplification requires that I combine like terms:

`(20+2k)/(3k+12)`