The equations in Exercises 79–90 combine the types of equations w...

Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.

4/(x^2 + 3x - 10) - 1/(x^2 + x - 6) = 3/(x^2 - x - 12)

Accepted Answer

So this equation tells us to determine whether the equation is an identity conditional equation or inconsistent equation. After solving the equation. So let's go ahead and try and solve this equation. Look here we write this, we have one. Overexpose five plus nine. Over x minus seven. That is equal to eight over X plus five X minus seven. Now we want to try and get rid of these fractions to do that. We're gonna multiply everything by the least common denominator. So if you look here all these common denominator we can kind of tell based on our fractions here we can multiply the two denominators at the bottom to get our L. C. D. So if I said the L. C. D. Is equal to X plus five times x minus seven we can work with this. So I'm gonna multiply everything in our equation by R. L. C. D. So multiply this by X plus five Times X -7. same thing here exports five Times X -7. And finally it's fine. X men seven. Okay so now that we see this we can start crossing stuff out. So if you look here we have an X plus five here on the top and an X plus five on the bottom. Those are going to cancel out. So those go away. Similarly here we have an x minus seven on the top x minus seven on the bottom, cancel those out. And finally over here on the right side we have X plus five. X minus seven up here and X five X minus seven on the bottom, cancel those out now. We can go ahead and rewrite this. We will have X -7 Left Times one plus nine Times X. Horse five equals to eight. And so you can go ahead and simplify this now. X minus seven plus nine, X plus 45. After distributing equal to eight and we'll go on a simple five and more. We add seven. Actually, that's the 45. Before you do that. It was negative seven plus 45. That will give us X plus nine X. And that is plus 38 Equals eight. subtract 38. Go ahead, write it this way and we get X plus nine X equals negative 30 and 10 X equals negative 30. Finally, just divide both sides by 10 ticket X equals -3. So we actually found one solution to our equation. So if we have one solution to our equation only. This is a conditional equation. I mean the answer to our problem is answer A. Alright. I hope to help you solve the problem. Thank you for watching. Goodbye

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