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# what is the lowest common denominator of 3/10x + 10 and x/5x^2 -5 ?

### 2 Answers by Expert Tutors

Julia K. | Tutor English, Math - any level; Russian backgroundTutor English, Math - any level; Russian...
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Dear Lola,

I assume I am reading it correctly: there are 2 expressions:

1st: three over ten x plu ten

2nd: x over five x square minus two.

If this is so, then here is your answer. (I am putting in brackets when it comes to operations in either denominator or numerator so that there is no mis-reading).

Step 1: make both expressions into fractions.

Step 1.a.: 3 / (10x) + 10 = 3 / (10x) + (10*10x) / (10x) = {because 10 whole can be seen as 10 times (10x)/(10x). When you multiply by 1, the number does not change. In our case we view 1 as fraction (10x)/(10x).} = (3 + 100x) / (10x)

Step 1.b.: x / (5x^2) - 5 = {cancel the x first, as it is present in both numerator and denominator. In numerator x can be seen as x^1, and in denominator we have x^2. The lowest power is 1, so we reduce by x^1} = 1 / (5x) - 5 = {now repeat the first step in Step 1.a. for this expression}=1 /(5x)-(5*5x)/(5x)=

= (1-25x) / (5x).

Step 2.: Find lowest common denomintaor.

We have 2 denominators: 10x and 5x. Although itmay seem that we can reduce 10x to 5x, we cannot. The numerators are not alike and no reduction of either is possible. Therefore, we have to go the opposite way - increase 5x to 10x. We have to multiply 5x by 2. So,

Step 3.: Answer: LCD = 10x