Video: Solving Rational Equation

Solve 2/𝑥 + 1/3 = 1.

01:51

Video Transcript

Solve two over 𝑥 plus a third equals one.

So in this question, what we’re looking to do is actually find out the value of 𝑥. In this case, we’ve got two over 𝑥 plus a third equals one. Well, the first step is to actually subtract a third, so we have two over 𝑥 is equal to two-thirds. And we get that because if we subtract a third from two over 𝑥 plus a third, we just get two over 𝑥. And if we subtract the third from one, we get two-thirds. And that’s because if you have a one minus a third, it’s the same as three-thirds, cause one is three-thirds, minus a third, which will give us two-thirds.

Okay, great! So now just an inspection, we can see that 𝑥 must be equal to three. That’s because we’ve got something that says two over 𝑥 is equal to two-thirds. So therefore, as we’ve got the same numerator, the denominators must also be the same. So therefore, we say the solution is 𝑥 equals three.

Okay, fab! We found the solution, but what we want to do is actually double check that. And we can do that by solving the equation by multiplying through. So let’s carry on and do that and see if we get the same answer.

So if we multiply each side of the equation by 𝑥, we’re gonna get two is equal to two 𝑥 over three. That’s cause two over 𝑥 multiplied by 𝑥 gives us two. And then if we multiply the right-hand side of the equation by 𝑥, we get two 𝑥 over three. And now if we multiply each side of the equation by three, what we get is six is equal to two 𝑥.

So finally, the last stage is to actually divide each side of the equation by two. And when we do that, we get three is equal to 𝑥, which matches the answer we thought, which is 𝑥 equal to three. So therefore, we can say that the solution of two over 𝑥 plus a third equals one is 𝑥 equals three.

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