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didacta special:
25% OFF, on all yearly plans
Use code
didacta25
at checkout
*Discount applies to first year only
0:06 → 0:12
In part one, we saw how to simplify algebraic fractions and how to add and subtract them.
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We discovered that they follow the exact same principles as numeric fractions.
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In this video, we're going to look at how to solve problems involving algebraic fractions.
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When solving, we could treat them as fractions and make the same denominator to add or subtract.
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But it's much easier to cross multiply, to get rid of the denominators completely.
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So this is the method I'll focus on in this video.
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Let's jump straight in with an example.
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To get rid of the three X minus two and the X plus four denominators, we just need to multiply them both up.
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We multiply everything by three x minus two.
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But on this side, the multiplied by and divide by just cancel out.
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But do keep in mind for future questions: Multiply everything in the question.
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So now we need to multiply everything by X plus four.
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Can you carry on to complete the rest of the question?
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Pause the video solve for X and click play when you're ready.
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Did you get x is 6?
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Quite often when solving algebraic fractions, we might end up with quadratics, which means we'll get two different values of X.
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So let's have a look at an example.
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So we start by multiplying up the two X minus four and the 20 minus two X to both sides.
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Can you carry on to solve the rest of the question?
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You'll have to collect everything together onto one side to make a quadratic,
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which you can then factorize and solve.
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Pause the video, work out the answer and click play when you're ready to check.
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Did you get x equals negative six and x equals five?
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It's really good practice to go back and check your answers by substituting them in.
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So if we substitute x is five into the original question,
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we get 3/6 equals 5/10.
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So a half equals a half, which means five is the correct answer.
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We should also do the same for x is negative six.
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So here's one last question for you to do, remember how I said you multiply everything by the denominators.
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Don't forget the negative one - pause the video solve for X and click play when you're ready to check.
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Did you get x is three and x is two?
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And did you double check your answers by substituting them into the original question?
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So there we have solving with algebraic fractions.
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There's nothing new to learn, we just make use of our algebraic skills.
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And you must remember to multiply everything by the denominators.