SOLUTION: 5. IF A CERTAIN NUMBER IS ADDED TO BOTH THE NUMERATOR AND THE DENOMINATOR OF THE FRACTION 7/9, THE RESULT 5/7.
7. THE SUM OF THE RECIPROCALS OF TWO CONSECUTIVE EVEN INTERGERS
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Question 120464This question is from textbook
: 5. IF A CERTAIN NUMBER IS ADDED TO BOTH THE NUMERATOR AND THE DENOMINATOR OF THE FRACTION 7/9, THE RESULT 5/7.
7. THE SUM OF THE RECIPROCALS OF TWO CONSECUTIVE EVEN INTERGERS IS 5/12. FIND THE INTERGERS.
This question is from textbook
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
5. let x=the number to be added, then we have:
(7+x)/(9+x)=5/7
7+x=5
x=-2
or
9+x=7
x=-2
another way:
Multiply each side by 7(9+x)---the LCM
7(7+x)=5(9+x) get rid of parens
49+7x=45+5x subtract 7x and also 45 from both sides
49-45+7x-7x=5x-7x collect like terms
4=-2x divide both sides by -2
x=-2
CK
(7-2)/(9-2)=5/7
5/7=5/7
7.
Let x=one even integer; reciprocal=1/x
and (x+2)=the other; reciprocal=1/(x+2)
Now we are told that:
(1/x)+1/(x+2)=5/12 Multiply each term by 12(x)(x+2)
12(x+2)+12x=5x(x+2) get rid of parens
12x+24+12x=5x^2+10x simplify
24x+24=5x^2+10x subtract 24x and also 24 from both sides
24x-24x+24-24=5x^2+10x-24x-24 collect like terms
5x^2-14x-24=0 quadratic in standard form---solve using the quadratic formula:
---------------------------------One integer
-----------------------------------------The other integer
and
----------------------Not an integer
CK
1/4+1/6=5/12
3/12+2/12=5/12
5/12=5/12
Hope this helps---ptaylor
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