Question 117496
Let the integers be x and x+1
1/x + 1/(x+1) = 7/12
12(x+1)+12x=7x(x+1) Multiply each side by 12x(x+1) to eliminate fractions.
12x+12+12x=7x^2+7x
7x^2-17x-12=0
7*-12=-84 What factors of -84 when added equal -17? Ans.: -21, 4
7x^2-21x+4x-12
7x(x-3)+4(x-3) Factor by grouping.
(7x+4)(x-3)=0
x=3 only answer that is an integer.
3, 4 Ans.
.
Check:
1/3 + 1/4
=4/12 + 3/12
=7/12
.
Ed