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The denominator of a fraction is 1 less than three times the numerator. If the numerator is increased by 1 and the denominator is decreased by 2 the resulting fraction is $1 / 2$. Determine the original fraction.

$$5 / 14$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Campbell University

McMaster University

Baylor University

Idaho State University

Lectures

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SUBTRACTING FRACTIONS Subt…

Okay, So for this question, we have way have, ah fraction and which were given the fact that a denominator of the fraction it's one less three times the numerator and the numerator if we increase it by one in the nominators decreased with two. The resulting fraction is 1/2. So we're gonna be using linear equations to solve this because the unknowns that were given are raised to the power of one. We also have to remember the additions of charge and under each other and multiplication division also under each other. So to begin with, were given that why three X minus one. So how do we get this? Well, we have our fraction, which is X over wine, our numerator and our denominator. And we know that why is three times bigger than X? Less than one were also given the fact that in the numerator and the denominator, if we make some slight changes, it can equal have 1/2. When we do this by adding plus one the top and then subtracting minus two to the bottom. And if we do that, we get half way, have enough information to solve this problem. We're simply going to plug in this white value. We're gonna replace this Why? With the three X minus one and where we can do that because we know exactly what bias. Now we have X plus one divided by three X ways one means to equals. We'll simplify this a little bit further down because three X minus one minus two is just three X minus three. So what, We replace this with minus three, and now we're given X plus one divided by three X minus three equals have Yeah, and we can simplify this a little bit further down by multiplying both sides of the equation with three X minus three and then the other side of the equation to we're gonna multiply by three. Explain history that's gonna cancel out the three X Ministry on the left side. We're gonna be left with X plus one is equal to three X and has three divided by two. And we're going to get rid of the two by multiplying into both sides of the equation. So we have one or two things to which is just gonna be one we're gonna look the flight to over here, too. So now we're going to distribute the to to the parentheses, so we're gonna have to X plus two people could three X minus three again to cancel out. So now we have two X Plus two equals three x ministry. We're going to get rid of the Twix and on that side and went to the right side three x on this train minus collects. And we're going to simplify this a little bit further down, so we're gonna have to was X minus tree by further down by shifting the negative three to the website by adding adding three to both sides of the equation. Yeah, and now we're gonna have five equals. X for numerator is X and sure so five both plug this five to the original equation while he goes three x minus one and we'll see that it is going to be why is equal to three times five is 15 minus one is 14. Why is secretly 14? So why is equal? Sure 14 in our question is asking us to determine the original fraction. So the original fraction is simply the X over wine or simply 5/14

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