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.

1/(x - 1) + 5 = 11/(x - 1)

Accepted Answer

So this problem says that for the following rational equation, the variable is contained in the denominator that we notice there are variable X is in the denominator on both sides of the equal sign, solve the equation and indicate the value. That makes the denominator zero. Some school hasn't right side. First I have nine Over X - plus one Equals two Over X -4. So I want to solve for X To do that. We notice here we have an X -4 on the bottom and the denominator for two different factions. I'm going to multiply everything By X -4. This will help us get rid of the denominator on the bottom. Now since I'm doing it to everything, I also have to multiply it by the one. So right here I'm gonna put Times X -4 About the one. So now we can cancel some stuff out. You notice here we have an X plus four on the bottom, x minus four on the bottom and x minus four on the top, cancel those out on the right side. We all said the same thing, I wish to be left but just not. and in the middle we will have X -4 times one. So that would be Plus X -4. Finally on the right side we're just left with two. So I can do some simplification. We have nine minus four on the left side, nine minus four gives us five plus x And we have two on the other side. Now I can subtract five And we get x equals negative three. So the solution to our equation is x equals negative three. Now we also want to check to see what value makes the denominator zero. So to do that we're going to set the denominator of our equation equal to zero. So if you notice our denominator is X -4 here and X -4 there. So we only have to check it once. So I say X -4. Set it equal to zero. We're gonna find what value will make this zero by solving for X. We add force both sets, We get x equals four, many of that. The value that makes it zero as X equals four. So people like hear our answer is answers. See where solution is negative three and divide the mixed kilometer zero is four. Okay, thank you for watching. I hope to help you solve the problem. Goodbye.

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