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Perform the indicated operation. Simplify, if possible.$$ rac{x}{x-4}- rac{3}{16-x^{2}}$$...

Question

Perform the indicated operation. Simplify, if possible.$$ rac{x}{x-4}- rac{3}{16-x^{2}}$$

Perform the indicated operation. Simplify, if possible. $$ \frac{x}{x-4}-\frac{3}{16-x^{2}} $$



Answers

Perform the indicated operation. Simplify, if possible. $$ \frac{x}{x-4}-\frac{3}{16-x^{2}} $$

So the question wants us to simplify this algebraic expression that we have here. And so to do this, we're gonna have to multiply X to the 1/4 uh, by two x to 3/4 as well as by minus X to the one for. So I started the first part. So x to the 1/4 times two x to the three. Fourth is equal to two x the 4/4 or two x And remember, when we're multiplying numbers with same base but different exponents, all we need to do is add the exponents together. And so this is what we're doing here. So 1/4 plus 34 it's is +44 It's which is just one. So we're just left with two backs here now, when we won't apply ex the one force times minus X to the 1/4. We do the same sort of addition with the exponents again. And so we'll end up getting minus extra meat 2/4 which is same thing as minus X to the 1/2. So when we add these two terms together, we'll get that Theis simplified algebraic expression. Of this one appear is two x minus root X and root. X is the same as extra power of 1/2

We're being asked to simplify 16 raised to the three force power. Now, unlike other problems, we can't just figure out what number times itself four times is equal to 16. Because our new Marie there is no longer one. So what we need to do is we need to rewrite our new Marie there. So, what is the one? However we know that one dwarf post 14 plus 14 physical, three Forbes. So what we can do is we can rewrite our problem to 16 to the 1/4 times 16 to the 1/4 time, 16 to the 1/4. Because, remember, we multiply like basis. We simply add their exponents. Well, now we first need to figure out what 16 raised to the 14 power is meaning what number times itself four times is equal to 16. Well, in that case, it's equal to two because two times, two times, two times two is equal to 16. So we're gonna have to times two times two. So now when we multiply two times two times two, we get eight. So what we've found is 16 race to the 3/4 power is equal to eat

Negative. Four ax times X cubed, squared. So I think I'd look at that power. The power first and that X cube squared is extent six guns, three temps to a six. Then we're multiplying now, so that's extra the first. So I looked at This is a negative four x to the seventh because we add the exponents. One plus six is seven when we're multiplying numbers of the same base.


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