In Exercises 1–34, solve each rational equation. If an equation h...

Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state.

1/x + 2 = 3/x

Accepted Answer

Welcome back. I am so glad you're here. We are asked to find the solution to the following rational equation. Otherwise saying no solution. Our rational equation is four divided by X plus six equals 16, divided by X. Our answer choices are answer choice, A X equals two, answer choice B X equals four, answer choice C X equals three halves and answer choice D no solution. I'll write when we are dealing with fractions, we're solving for X and we have an equal sign, we want to first get rid of the fractions. And in order to do that, we're going to multiply all of our fractions, everything by the least common multiple of our denominators. So with our denominators, X and X, what's the lowest number that they both multiply into? That's going to be X. So we're going to multiply everything by X. And then we take a look at our denominators and the X is they're being multiplied by and then we simplify. So for the first one, X multiplied by four divided by X, these XS cancel out and we're left with just four. For the next one X multiplied by six, there's nothing in the denominator to cancel out our X. So this is going to be plus X multiplied by six, which is six X and that's equal to on the right, we have 16, divided by X multiplied by X. And here again, the X is cancel out. So we're left with just 16, our fractions are gone. Yay. Now, we just want to get X by itself on one side of the equation and all of the numbers to the other side. So first we're going to move this four over here, the four is positive. So to move it, we are going to subtract four. What we do to one side, we do to the other on the left four minus four is zero. And all we have is the six X that's equal to on the right 16 minus four is a positive 12. Now that six is being multiplied by the X to get the X by itself, we need to move the six. The opposite of multiplication is division. So we're going to divide by six. What we do to one side we do to the other on the left six divided by six is one. So we have one X which is just X X is by itself. Yay. And that is equal to 12 divided by six which simplifies 22. So X is equal to two. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x + 2 = 3/x

Key Concepts

Rational Equations

Finding a Common Denominator

Checking for Extraneous Solutions

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