Question

the sum of the reciprocals of two consecutive even integers is 9/40. This can be represented by the equation shown.
1/x + 1/x+2 = 9/40 use the rational equation to determine the integers. show all work.

Answer 1

@jim_thompson5910 could u help with this??

Answer 2

multiply every fraction by 40x(x+2)

Answer 3

x and x+2 are NOT necessarily EVEN numbers. If you solve as you have it set up, it will only be luck that gives you even numbers.

Answer 4

i would add and then "cross multiply" i guess it is a matter of preference

Answer 5

well i did what @jim_thompson5910 said and multiplied each fraction by 40x(x+2) and I got 40x+80 and 80x^2+160x

Answer 6

would this be right??? @satellite73 @jim_thompson5910

Answer 7

1/x times 40x(x+2) = 40x+80

1/(x+2) times 40x(x+2) = 40x

9/40 times 40x(x+2) = 9x(x+2) = 9x^2+18x

Answer 8

1/x + 1/(x+2) = 9/40

becomes

40x+80 + 40x = 9x^2 + 18x

Answer 9

@jim_thompson5910 okay I see.. so where do we go from there?

Answer 10

get the equation into standard form, then use the quadratic formula

Answer 11

standard form for a quadratic is

ax^2 + bx + c = 0

Answer 12

@jim_thompson5910 so we use the quadratic formula on the equation you just found??

Answer 13

no you have to get it into the form ax^2 + bx + c = 0 first

Answer 14

@jim_thompson5910 okay so this is all i got ---> 9x^2+40x

Answer 15

40x+80 + 40x = 9x^2 + 18x

80x+80 = 9x^2 + 18x

0 = 9x^2 + 18x-80x-80

0 = 9x^2 - 62x - 80

9x^2 - 62x - 80 = 0

Answer 16

now you can use the quadratic formula

Answer 17

you can factor if you want, but it might take a while lol

Answer 18

@jim_thompson5910 okay so i got x= 8, -10/9

Answer 19

same here

Answer 20

so if x = 8, then x+2 = 10

Answer 21

1/8 + 1/10 = 9/40

5/40 + 4/40 = 9/40

9/40 = 9/40

Answer 22

works out, I'll let you check the other one

Answer 23

@jim_thompson5910 so the answer would be x=8 , and -10/9??

Answer 24

oh they have to be integers, so x = -10/9 must be ignored

Answer 25

so the two integers are 8 and 10

Answer 26

@jim_thompson5910 okay , thank you so much!

Answer 27

sure thing

Answer 28

@dan815 @Hero if u guys help me i will fan u and medal :P

Answer 29

@ytrewqmiswi

Answer 30

okie so i don't get how they got x=8 and x=10 in the end why did -10/9 change to 10?

Answer 31

help guys?

Answer 32

x = 8 or -10/9

since -10/9 is not an integer, ignore it.

Answer 33

thats the part i don't understand

Answer 34

what part, could you elaborate

Answer 35

helpful link - https://answers.yahoo.com/question/index?qid=20130513215652AAFLnSA

Answer 36

OMG THANKS MAN here a medal

Answer 37

oh and ur first fan :)

Answer 38

haha XD thanks :D

Answer 39

:P