Simplifying Fractions With A Variable Simplify: (1)/(P(1-(P)/(N))(1-(m)/(P)))

drobtinicnu 2022-09-11 Answered
Simplifying Fractions With A Variable
Simplify:
1 P ( 1 P N ) ( 1 m P )
To show that it is equal to:
N N m [ 1 N P + 1 P m ] .
I honestly have no idea how to even start the question. I am wondering if the question is asking to go backward, i.e. to go from the second part to the first, but it doesn't seem that way. If someone could show me how to do this or even get me started would be very helpful!
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Willie Smith
Answered 2022-09-12 Author has 18 answers
Hint
1 P ( 1 P N ) ( 1 m P ) = 1 ( 1 P N ) ( P m ) = N ( N P ) ( P m ) .
Then use partial fractions.
N ( N P ) ( P m ) = α N P + β P m
Expand the expression on the right and compare it with the expression on the left-hand side to determine α and β
Euler's trick: Instead of expanding the right-hand side you can also use Euler's trick. For example to obtain α multiply by the associated denominator N P and then set N P = 0 P = N to obtain:
N P m | P = N = α + N P P m | P = N β α = N N m

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-06-26
Negative/Positive Index Numbers
I came across a question that I was unable to solve, it involves positive and negative index numbers in the same fraction and I'm not sure how to solve that, if anyone could help me please??
( 7 a 5 b 3 5 a 6 b 2 ) ( 7 b 3 a 2 5 b 5 a 4 )
Also some working out would be great so I can see how to work it out properly. Thanks!
asked 2022-05-22
Prove that 1 1 + a 1 + a 1 a 2 + 1 1 + a 2 + a 2 a 3 + + 1 1 + a n 1 + a n 1 a n + 1 1 + a n + a n a 1 > 1.
I find it hard to use any inequalities here since we have to prove > 1 and most inequalities such as AM-GM and Cauchy-Schwarz use 1. On the other hand it seems that if I can prove that each fraction is > 1 that might help, but I am unsure.
asked 2022-04-10
Question on recurring decimal digits
In my discrete maths class, I have come across an interesting phenomenon for which I can't find an explanation!
If we divide 1 by 13 we obtain 0.07692307
If we divide 3 by 13 we obtain 0.23076923
If we divide 4 by 13 we obtain 0.30769230
As you can see, the digits are recurring in the same order but starting at a different point in the sequence.
Can someone explain this to me? What exactly is happening here?
asked 2021-12-20
What is 12 divided 1/4?
asked 2022-06-25
canceling double fractions how?
I had this example:
11 5 2 = 11 10
then:
2 1 5 2 = 11 10
1 5 11 10
is this right canceling of double equation?
asked 2022-09-20
Inequality with a+b+c=1
Let a , b , c be positive reals such that a + b + c = 1. Prove that
b c a + 5 + c a b + 5 + a b c + 5 1 4 .
Progress: This is equivalent to show that
1 a 2 + 5 a + 1 b 2 + 5 b + 1 c 2 + 5 c 1 4 a b c .
I'm not sure how to proceed further. Also equality doesn't occur when a = b = c, which makes me more confused.
Edit: The original inequality is as follows: Let a 1 , a 2 , , a n be n > 2 positive reals such that a 1 + a 2 + + a n = 1. Prove that,
k = 1 n j k a j a k + n + 2 1 ( n 1 ) 2 .
asked 2022-06-24
[ n 1 ] + [ n 2 ] + + [ n n ] + [ n ] is even
I tried this by taking two different cases, when, n is even and when n is odd. But I could not establish any relation between the two. Please help to solve this problem and thanks a lot in advance.
P.S. Although nothing is mentioned in the question I think [   ] stands for greatest integer function as otherwise the sum would be in a fraction which is not even as only natural numbers are regarded as even.