Exercises 41–60 contain rational equations with variables in deno...

Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.

(x - 2)/2x + 1 = (x + 1)/x

Accepted Answer

So this problem tells us for the following rational equation. That variable is contained in the denominator. So we have an equation there. You notice the Gs and the denominator for some of those rations solve the equation, indicate the value to mix the dominator zero. So let's go ahead and write this out, kev G -7/4 G plus seven equals G plus over two G. Now we want to get rid of the fraction so we can actually add these together and solve for gene to do that. We're going to find what the L. C. D. S. This is the least common denominator. So we look here we have a fraction of 4G and a fraction of 2G. I'm gonna go ahead and use the larger number here and say our LC. D. is 4G. Now we're going to multiply everything by L. C. D. The reason I didn't use two G is because to G give me multiplied by two to get four G. So two G does go into four G. So I'll show you right here multiply everything by L. C. D. Here, we have four G. You also have four G. On the seven and four G. Here let's go ahead and mark out all the stuff we don't need. So we have 4G on top 4G on bottom here. Those are gone. You have seven times four G which will just stay as that is. And we have sent over two G. So you have four G over two G. So those will cancel out. But that just leaves us with four number two which is two. Now we can go ahead and rewrite the skin. We now have G -7 left over. Then we have a seven times four G. Which is 28 G. And the other side we have G plus 10 multiplied by two. It's not just some five. And further we have G plus 28. G. Is 29 G. Then we have a negative seven. Still on the other side we have two G plus 20. Now we can move our constants over and our variables over. So on this side I'm gonna move my 2G over And then move by seven over to the other side. Look here we have 29 G minus two G. Which is 27 G. Then we have 20-plus 7 on the right side That is 27. Finally divide both sides by 27. I get G equals one. So the solution to our equation is G equals one. Now we can also find the value that makes it the denominator zero. So you notice here we have a four G. Here and a two G. Here let's set four G equal to zero and also set to G equal to zero. That will solve for G. Well if we do that we're four we get G equals zero. Same thing here divided by two. We get G equals zero. So the value that makes our denominator zero H. G equals zero. Many of that our answer is answer A. Okay that will solve the problem. Thank you for watching. Goodbye.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. (x - 2)/2x + 1 = (x + 1)/x

Key Concepts

Rational Equations

Restrictions on Variables

Solving Rational Equations

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