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Solving Rational Equations with Like Denominators - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Solving rational equations is substantially easier with like denominators. When solving rational equations, first multiply every term in the equation by the common denominator so the equation is "cleared" of fractions. Next, use an appropriate technique for solving for the variable.

Remember that an equation means you have an equal sign. And you're solving you're tying to find the value of the variable. In our case I'm probably going to be using x's like in this problem. Okay so when you start looking at equations that have denominators it can be really tricky unless all of the denominators are the same. If I have all the denominators the same like this, there's an idea I want you guys to think about, if I were to go through and multiply all 3 of these terms by 2, it'll be pretty much the same thing as just crossing out those denominators. Right if I multiply everything by 2 in this original equation then I would get this for my 3 terms. And now there's no fractions so I'm a happy camper.
I would subtract 3x from both sides and I can really easily get that x is equals to negative 1. That's a really great tool I want you guys to remember, when you're looking at your homework. I'm going to say it one more time, if all of your denominators are exactly the same, you can cross them out which is essentially like dividing all of those terms by that denominator. You can cross them out and just work with the numerators. Let me show you what that would look like if I had my variable in the denominator, you can do the same idea if I had like 3x over x plus 5 over x is equal to 8x squared over x. A lot of students who didn't know this trick would go through and they would reduce this fraction which is clever, they're on the right track. Other students might try to combine these fractions yeah because those are combinable fractions they have the same denominator.
But you guys this is the trick, these 3 terms all have exactly the same denominator, so I'm going to multiply everything by x and then just work with the tops. That can make your problems much easier when you're approaching them. Keep that in mind when you're going through solving rational equations. Especially if they all have like denominators.

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