Simplify each complex fraction. [ 3/(p^2-16) + p ] / [ 1/(p - 4) ...

Question

Simplify each complex fraction. [ 3/(p^2-16) + p ] / [ 1/(p - 4) ]

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem. We want to simplify this expression. That is really a big fraction. Where we have five divided by f squared minus 121 minus F in the numerator And one divided by F -11 in the denominator. So because we have this giant fraction with fractions in the numerator and denominator, I'm gonna work on simplifying the numerator separately from the denominator. So if we look at the numerator I have five divided by f squared minus 121 minus F. So I have this fraction and the second component standing alone and in order to simplify it, great to combine the two components. So that means I need to have the second component F have a denominator of f squared minus 121. So I can do that by multiplying the second component with f squared minus 121 divided by f squared minus 121. So when I do that this becomes five divided by f squared minus 1 21 minus f. Times of squared is up to the 3rd times of times negative 1, 21 is negative 121 F divided by Of Squared -121. And from here you can see that I now have the same denominator in both of those components. So I can combine the fraction To be five -F to the third. If I distribute this negative Plus F. That's being divided again by the common Denominator of of Squared -1, 21. So I've simplified the numerator of my fraction. So I need to bring back the denominator which is one divided by f minus 11. But you can see that I still have fractions in both the numerator and denominator, so I'm going to write this in the linear format for division to see if it makes it easier to simplify. So I'll move the denominator up to be the second fraction here and from here recall that I can change this division to be multiplication as long as I switched the numerator and denominator of the second fraction. So my second fraction will now become f -11 divided by one. Well, there doesn't seem to be anymore simplification, But if you think about 121, that is the same as 11 times 11 or squared. So f squared minus 121 can be written as f squared minus 11 squared. And this form looks very similar to the form for a difference of squares. When you think of X squared minus y squared, you can rewrite that as X plus y times x minus y. So I apply that same logic to f squared minus 11 squared, I can rewrite it as F plus 11 times F minus 11. And if I rewrite it in that form, F plus 11 times f minus 11, you can see that I now have f minus 11 in the denominator of my first fraction and the numerator of my second fraction. So I can actually cancel it out. So that leaves me with just negative F. To the third plus 121 F plus five divided by F plus 11. So I rearranged the numerator To have the highest degree 1st and you can see that I can't simplify this any further. So this becomes my final simplification. And if we look at the answer choices, you can see that answer choice A also has a negative F. To the third plus 121. F plus five divided by F plus 11. So hopefully this video helped and see you next time.

Simplify each complex fraction. [ 3/(p^2-16) + p ] / [ 1/(p - 4) ]

Key Concepts

Complex Fractions

Factoring Polynomials

Common Denominators

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