Question

(r^-1 + s^-1)^-1

Answer 1

\[\large (r^{-1}+s^{-1})^{-1}\]

Hmm ok let's start by establishing this.\[\large a^{-1} \qquad = \qquad \frac{1}{a^{1}}\]

Understand that part? We can change the exponent to positive by placing the base in the denominator.

Answer 2

Applying that rule gives us,\[\large (r^{-1}+s^{-1})^{-1} \qquad = \qquad \frac{1}{(r^{-1}+s^{-1})^1}\]

Answer 3

so in this case what would the base be?

Answer 4

so you have to turn it into a fraction right?

Answer 5

From here what we'll want to do is, again apply this rule to each r and s term `individually`. We'll ignore the 1 exponent on the outside of the brackets.

\[\large \frac{1}{r^{-1}+s^{-1}} \qquad = \qquad \frac{1}{\dfrac{1}{r^1}+\dfrac{1}{s^1}}\]

Answer 6

I'll put some brackets so it's easier to read.
\[\large \frac{1}{\left(\dfrac{1}{r}+\dfrac{1}{s}\right)}\]
From here, you need to get a common denominator among those fractions so you can add them together. This will allow you to further simplify it down.

Let me know if you're still confused.

Answer 7

ok

Answer 8

how will you find the common denominator

Answer 9

Sorry I didn't see your message til just now :D Website must be lagging.

Yah we want to simplify it down to a nice clean fraction. Without the complex form that it's in now, (fraction within a fraction).

Answer 10

ok i get it now

Answer 11

Oh got it? c: cool.

Answer 12

how can i break it out of the complex fraction that it is in now

Answer 13

To get a common denominator, the left fraction will need a factor of \(\large s\) while the right fraction needs a factor of \(\large r\).

\[\large \frac{1}{\left(\dfrac{1}{r}+\dfrac{1}{s}\right)} \qquad = \qquad \frac{1}{\left(\dfrac{s}{rs}+\dfrac{r}{rs}\right)}\]

Answer 14

Now that they have the same base, we can add them together.\[\large \frac{1}{\left(\dfrac{s}{rs}+\dfrac{r}{rs}\right)} \qquad = \qquad \frac{1}{\left(\dfrac{r+s}{rs}\right)}\]

Answer 15

okay