Help me divide this rational expression please

Question

1/x+5 over 3x/x^2-25

Answer 1

1/x+5 over 3x/((x^2)-25)

 

1/x+5 times ((x^2)-25)/3x

 

1/x+5 times (x+5)(x-5)/3x

 

(x-5)/3x

 

 

For dividing fractions, here's a useful phrase to help you remember what to do: "Dividing fractions is easy as pie, flip the second and multiply."

 

For example, say you have 1/2 over 1/3. That becomes 1/2 times 3/1, which equals 3/2. Or say you have 3/4 over 2/3, that becomes 3/4 times 3/2, which equals 9/8.

 

In this case, you take the second fraction, 3x/((x^2)-25), flip it upside down so that it's ((x^2)-25)/3x, then switch to multiplication so that now it's  1/x+5 TIMES ((x^2)-25)/3x. From there you factor ((x^2)-25), the (x+5) cancels out with the (x+5) in the denominator of the first fraction, and you're left with (x-5)/3x.