In order to find the difference of any two rational expressions, you need to first make sure they have common denominators. I’m lucky because these guys already do. My common denominator for both of them is m² plus 3m plus 2. That’s going to be the bottom of my fraction.
The top is just going to come from subtracting these, but I need to be really careful with this subtraction sign. That negative is going to be distributed on both of those terms. I bet you money that if you’re getting these homework problem incorrect, the reason why is because you’re not distributing that negative sign.
Here is what I mean. I’m going to start with 7m minus 2 for my first fraction, then I need to subtract 5m most students get that, but people are going to write minus 6 because look And there it is minus 6, but we’re not subtracting 6, we’re subtracting -6. Please write that carefully. From there it’s pretty straight forward. Combine like terms on the top of your fraction 2m plus 4 over m² plus 3m plus 2, and then I’m going to factor both the top and bottom and look for any expressions that can be cancelled out. M plus 2 and m plus 1 sweet my m plus 2s are eliminated and I’m left with just 2 over m plus 1. That’s my simplified version of this difference. Be really, really careful with that subtraction sign any time you’re subtracting rational expressions that’s where students make their mistakes.
The last thing I want to leave you with is thinking about excluded values. Remember an excluded value is any value of the variable that would make this denominator equal 0. Well luckily it’s pretty easy to find I already have my denominator in factored form and I could see that this would be equal to 0 if m were equal to -2, or if m were equal to -1. Those are going to be my excluded values. Along with my simplified answer an A+ student would write the excluded values, the things that could not be because if m took on these values, my original fractions would be undefined.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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