Question

25/28m and 5/12m-20

find the least common denominator for the following pair of rational expressions

Answer 1

is 56 correct??im not preety sure

Answer 2

You could multiply the two denominators to get a common denominator but that would not be the lowest one in this case I think. To get the lowest one first make sure you factored both denominators fully (down to prime numbers). The first fraction would then be:

\[25/ (2*2*7)\]

The second one is a bit more difficult. You have to factor it as a binomial. Take out the greatest common factor which is 4, so it becomes:

\[5/(4(3m-5))\]

but the four can be further factored in to 2*2. So the final factored form is:

\[5/(2*2(3m-5))\]

Now that both fractions are factored look at all the factors for both of them. We have:

2, 2, and 7 from the first one, and 2, 2 and 3m-5 from the second one. The least common denominator always will have only one of each factor in it. If there is a factor that the two fractions share you only use it once. So they share a 2, we use one of them, they share another 2 we only use one of them. If they do not share a factor you must use it in the least common denominator. So, the 7 and 3m-5 must also be used. Multiply those four numbers together and you get your least common denominator

2*2*7*(3m-5)= 28(3m-5)

Your answer is 28*(3m-5)!

Hope it helps some. The last part is hardest.

Answer 3

Sometimes making a factor tree for each of the denominators helps with that last part.