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C3 product rule differentiation help

I have the following question.
The guided answer is also given.

Now why is there a common factor of (5x-1)-2 given when the only common factor I can see is (5x-1)-1 to leave a (5x-1)2 ?

HELP

This is in the second-to-last step of the guided answer.
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Screen Shot 2016-09-12 at 19.26.05.png8.1KB
Original post by nwmyname
I have the following question.
The guided answer is also given.

Now why is there a common factor of (5x-1)-2 given when the only common factor I can see is (5x-1)-1 to leave a (5x-1)2 ?

HELP

This is in the second-to-last step of the guided answer.


Not sure if I understand what you're asking for.

They factored out the one with exponent of -2 because it gets rid off any fractions within then next bracket...?
Reply 2
Avatar for Zacken
Zacken
22
Original post by nwmyname
I have the following question.



Maybe it'd be better if you wrote it as fractions.

−15x2(5x−1)2+6x5x−1=−15x2(5x−1)2+6x(5x−1)(5x−1)2\displaystyle \frac{-15x^2}{(5x-1)^2} + \frac{6x}{5x-1} = \frac{-15x^2}{(5x-1)^2} + \frac{6x(5x-1)}{(5x-1)^2}

YAY! Now we have common denominators! (Remember, when adding fractions, you need common denominators - think back to GCSE!)

Now add the fractions (and factorise the numerator) and you get what the answer gets, just in fraction form rather than index form.
(edited 7 years ago)
Reply 3
Avatar for nwmyname
nwmyname
OP
13
Original post by RDKGames
Not sure if I understand what you're asking for.

They factored out the one with exponent of -2 because it gets rid off any fractions within then next bracket...?


Got it.
(edited 7 years ago)
Reply 4
Avatar for nwmyname
nwmyname
OP
13
Original post by Zacken
Maybe it'd be better if you wrote it as fractions.

−15x2(5x−1)2+6x5x−1=15x2(5x−1)2+6x(5x−1)(5x−1)2\displaystyle \frac{-15x^2}{(5x-1)^2} + \frac{6x}{5x-1} = \frac{15x^2}{(5x-1)^2} + \frac{6x(5x-1)}{(5x-1)^2}

YAY! Now we have common denominators! (Remember, when adding fractions, you need common denominators - think back to GCSE!)

Now add the fractions (and factorise the numerator) and you get what the answer gets, just in fraction form rather than index form.


You missed a -15 on the second part on the right hand side of the equal sign.

Thanks very much!
Original post by nwmyname
I'm kind of getting you but why -2? I mean from a -1?


What do you mean? I still don't follow.

Because then the -1 goes into a 1 rather than a 0. At some point you'd have to deal with the extra fraction anyway so factoring out the -2 exponent deals with it in one go.
Reply 6
Avatar for Zacken
Zacken
22
Original post by nwmyname
You missed a -15 on the second part on the right hand side of the equal sign.

Thanks very much!


Thanks, I'll edit it. Anywho, the moral of this is that if something is unclear in a particular form - rewrite it in another form and see if makes any sense.
Reply 7
Avatar for nwmyname
nwmyname
OP
13
Original post by RDKGames
What do you mean? I still don't follow.

Because then the -1 goes into a 1 rather than a 0. At some point you'd have to deal with the extra fraction anyway so factoring out the -2 exponent deals with it in one go.


Sorry haha my reply got edited late.
I was meant to say 'Got it!'

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