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Simplify the function π of π₯ is equal to nine π₯ plus 72 over π₯ plus one divided by nine π₯ plus 72 over five π₯ plus five.
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Okay.
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So this is a dividing fractions question.
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And when dividing fractions, we actually flip the second fraction and turn it into a multiplication.
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So we can say π of π₯ is equal to nine π₯ plus 72 over π₯ plus one times five π₯ plus five over nine π₯ plus 72.
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Now I like to put parentheses around each of my numerators and denominators to just identify the fact that theyβre separate terms.
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And then we can see that in the numerator of the first fraction, weβve got nine π₯ plus 72.
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In the denominator of the second fraction, weβve got nine π₯ plus 72.
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So in multiplication of fractions, we multiply the numerators together, we multiply the denominators together.
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I can do some cross canceling here.
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So if I divide nine π₯ plus 72 by nine π₯ plus 72, I get one.
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If I divide nine π₯ plus 72 by nine π₯ plus 72, I also get one.
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So I can now say that π of π₯ is equal to one over π₯ plus one times five π₯ plus five over one.
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And now I can see that I can factor this numerator here.
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Theyβve both got five as a common factor.
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So Iβm gonna take that out of that numerator.
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And five times π₯ is five π₯, and five times positive one is positive five.
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So now I can see that Iβve got a common factor of π₯ plus one on the top and on the bottom of those fractions.
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π₯ plus one divided by π₯ plus one is just one, and π₯ plus one divided by π₯ plus one is just one.
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So Iβve now got one times five times one on the numerator and one times one on the denominator.
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Well that simplifies to five over one or just five.
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So weβve simplified that function down to π of π₯ is equal to five.