How do you find two consecutive even integers, the sum of whose reciprocals is 3/4?

1 Answer
Jun 26, 2016

#1/2 + 1/4 =3/4#

Explanation:

Let the first number be #x#
The second is #x+2#

#1/x+ 1/(x+2) = 3/4#

#color(red)(4x(x+2)xx1)/x + color(red)((4x(x+2)xx1)/((x+2))#
= #color(red)((4x(x+2)xx3)/4 " multiply by" color(red)(4x(x+2)#

#color(red)(4cancelx(x+2)xx1)/cancelx + color(red)((4xcancel(x+2)xx1)/(cancel(x+2))#
= #color(red)((cancel4x(x+2)xx3)/cancel4 " multiply by" color(red)(4x(x+2)#

#4(x+2) + 4x = 3x(x+2)#

#4x + 8 +4x =3x^2 + 6x#
#3x^2-2x-8=0#

#(3x+4)(x-2)=0#

#x=2 or x = -4/3 "(reject)"#

The numbers are 2 and 4.
Check:
#1/2 + 1/4 =3/4#