In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (...

Question

In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)

Accepted Answer

hey everyone here are asked to add or subtract as indicated in the expression three divided by four X squared minus three divided by five X. Now before we can subtract these two fractions, we need to find a common denominator. So to do this, we want to start out by looking at the fact that is given by each of the denominators. So from the first expression we have four and X squared and from the second we have five and X. Now from here we can start looking for our least common denominator. Now we can start by looking at the four and five and there's nothing that is divisible by both of them. So we can just multiply them together to get our coefficient of 20 and we can move on to our X variable. And we want to note that both denominators are mono meal. So our variable for our denominator will be the one with the higher exponents. So in this case it is X squared. So our least common denominator here is 20 X squared. And we can now move on to adjusting the two expressions to have this denominator. So starting with the first expression of three divided by four X squared. We know to get 20 X squared, we have to multiply this four X squared by five. So we need to multiply both the numerator and the denominator by five. And then this gives us 15 divided by 20 X squared. So from here we can move on to the next expression of three divided by five X. And to get 20 X squared from five X we need to multiply by four X. So we have to multiply both the numerator and the denominator by four X. This gives us 12 X divided by 20 X. Squared. And from here we can subtract since they both have the same denominator. So from our first expression we have 15 and from our second we have minus 12 X. All over this 20 X. Squared. And now we can simplify this because both 15 and 12 are divisible by three. So we can factor it out which gives us three times the quantity of five minus four X divided by 20 X. Squared. And this is our answer here. Of choice C. Thanks for watching. I hope you found this video helpful. And I'll see you again next time.

In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)

Key Concepts

Rational Expressions

Finding a Common Denominator

Combining and Simplifying Rational Expressions

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