Exercises 57–59 will help you prepare for the material covered in...

Question

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: 3/(x−4) − 2/(x+2).

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression eight over x minus three minus five over X plus six. And we are asked to find the difference. Well when we need to subtract two fractions, they need to have a common denominator. So what would our common denominator be here? Well they both have these factors X minus three and a different factor here. X plus six. And the common denominator for those two would actually be the two factors multiplied by each other X plus six times X minus three. And so how do we get from eight over X minus three to having this X plus six times X minus three in the denominator. Well the difference is this X plus six. So we're going to multiply the denominator by X plus six and we're going to multiply the numerator by that as well because X plus six over X plus six is one. So we're just multiplying it by one. That's how we get that denominator for the first one. How about five over X plus six. Well the difference there is that x minus three. So likewise we're going to multiply this second fraction by x minus three over x minus three and that's how we get that common denominator. Now we can copy down the numerator. The first numerator is going to be eight times the X plus six and the second fractions numerator is five times x minus three Now we could combine them because they have a common denominator. But I'm first going to distribute the number in front of the parentheses for each numerator. So eight times X. Is eight x. Eight times six is plus 48 Over our X-plus six times X -3 minus five times X is five X. And five times negative three is minus 15 over the X plus six x minus three. Now we have a common denominator and we can combine our numerator. So eight X plus 48. And now this is very important. This minus needs to be applied to both terms in the numerator of our second fraction. So it will be minus five X and minus negative 15 which is plus 15 All over the X-plus six times X -3 common denominator. Now we can combine like terms in the numerator, that would be the eight X. And the minus five X. And the 48. And the plus 15 combining those eight x minus five X. Is three X. 48 plus 15 is plus 63 divided by R X plus six times X minus three. And looking at our numerator we could factor a three out both terms have a three in them. So that would be X three times X plus but neither denominator factor is three or X plus 21 so it won't cancel out anything. So there's no need to factor out that three. And we can leave our answer as three X plus 63 divided by X plus six times X minus three. We look at our answer choices in this matches with answer choice a well done, we'll catch you on the next one.

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: 3/(x−4) − 2/(x+2).

Key Concepts

Rational Expressions

Common Denominator

Simplifying Expressions

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