Question

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Answer 1

Answers:

LCD needed to combine the variables:  15

LCD needed to combine the constants:  21

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Explanation:

If two numbers m and n do not have any common factors (other than 1), then the LCM is m*n. We simply multiply the values.

So for example, the LCM of 2 and 3 is 2*3 = 6.

For the variable terms, the denominators are 5 and 3. So the LCM is 5*3 = 15, and this is the LCD of those variable fractions.

Similarly, the LCD of the constant terms is 21 because 7*3 = 21.

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Again, for all of these examples, the two values had no factors other than 1 in common. If you were dealing with something like the LCM of 8 and 12, then the LCM would not be 8*12 = 96. But we can fix things by dividing that by 4 to get 96/4 = 24 which is the true LCM here.

So the more generalized formula would be (m*n)/(GCF of m and n)

This formula works for the previous section because the GCF was 1.

Answer 2

When they ask for combining the variable terms, you take one of the variable terms and move to the other side of the equation and change its sign. From there, you cross multiply those variable terms and simplify. Once you simplify, you look at the denominator and that will be your answer.
Similarly for the constant terms, you take one of the constant terms and move to the other side of the equation and change its sign. Again, you cross multiply these two constant terms and simplify. The denominator you get after simplification will be your answer.