Question

PLEASE HELP

Find all pairs of positive unit fractions that add up to 1/8

Answer 1

P₁(1/9; 1/72)

P₂(1/10; 1/40)

P₃(1/12; 1/24)

P₄(1/16; 1/16)

Explanation:

(1/m) + (1/n) = 1/8

(m+n)/(m*n) = 1/8

8*(m+n) = m*n

8m + 8n = m*n

8m – m*n = -8n

m (8-n) = -8n

m = 8n / (n-8)

If

n = 9

m = 8*9 / (9-8) = 72

then

(1/72) + (1/9) = 1/8

If

n = 10

m = 8*10 / (10-8) = 40

then

(1/40) + (1/10) = 1/8

If

n = 12

m = 8*12 / (12-8) = 24

then

(1/24) + (1/12) = 1/8

If

n = 16

m = 8*16 / (16-8) = 16

then

(1/16) + (1/16) = 1/8

Finally, the pairs of positive unit fractions that add up to 1/8 are

P₁(1/9; 1/72)

P₂(1/10; 1/40)

P₃(1/12; 1/24)

P₄(1/16; 1/16)