Add or subtract, as indicated. See Example 4. (5/12x²y) - (11/...

Question

Add or subtract, as indicated. See Example 4. (5/12x²y) - (11/6xy)

Accepted Answer

Welcome back. Everyone in this problem, we want to perform the indicated operations on nine divided by 10 M squared P minus divided by five MP. For our answer choices, A is negative 17 divided by M PB is negative 17 M divided by 10 P squared C is nine minus 26 M all divided by 10 M squared P and the D is 26 M minus nine all divided by two M squared P. Now, what do we know here? Well, we're trying to work out what's going on with these algebraic fractions and we treat algebraic fractions in the same way that we treat regular fractions. We need to find an LCM and then we can go ahead and combine them. So let's think what's the LCM of 10 M squared P and five P? Well, if you look at both expressions, notice that five P can go into 10 M squared P because five is a factor of 10 and P is a factor of P. So our LCM would be 10 M squared P. So let's rewrite both fractions with a denominate common denominator of 10 M squared P. Well, nine, the denominator for our first expression is already 10 M squared P. So I can rewrite nine. But for our second expression, five MP goes into 10 M squared P two M times. And, and let me just show you that. So if we have 10 M squared P and we're factoring five MP O OK, five goes into 10, 2 times. M goes into M squared M times and P goes into P one time. So that's why the common factor would have been two M. So we can multiply our numerator by two M and 13 multiplied by two M equals 26 M. Now, if we're looking at our fraction, is there any common factor that we can simplify to get it any further? Well, there's no common factor between nine and negative 26 M. So this means our expression is in its simplest form. And if we look at our answer choices, that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

Add or subtract, as indicated. See Example 4. (5/12x²y) - (11/6xy)

Key Concepts

Finding a Common Denominator

Simplifying Algebraic Fractions

Combining Fractions by Addition or Subtraction

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