Let A , and B represent the numbers.

A + B = 10

1/A + 1/B = 5/12

Find the common denominator for

A, B which is AB by multiplying B by 1 and A, and multiplying A by 1 and B

The second equation will be

(A+B)/AB = 5/12

we know that A+B = 10

You now have 10/AB = 5/12

cross multiply and solve for AB

10x12=5AB

120 = 5AB divide both sides by 5

24 = AB

We now have A + B = 10

AB = 24

Divide both sides by B

A = 24/B

Substitute A in Equation 1

24/B + B =10

Multiply each term by B

24 + B^2 = 10B

Subtract 10B from both sides

B^2 -10B +24 = 0

(B-6)(B-4) = 0

B= 6, and B=4

If B = 6, then A =4

Your two numbers are 6 and 4.

(B + A)/AB = 5/12

A + B = 10

1/A + 1/B = 5/12

Find the common denominator for

A, B which is AB by multiplying B by 1 and A, and multiplying A by 1 and B

The second equation will be

(A+B)/AB = 5/12

we know that A+B = 10

You now have 10/AB = 5/12

cross multiply and solve for AB

10x12=5AB

120 = 5AB divide both sides by 5

24 = AB

We now have A + B = 10

AB = 24

Divide both sides by B

A = 24/B

Substitute A in Equation 1

24/B + B =10

Multiply each term by B

24 + B^2 = 10B

Subtract 10B from both sides

B^2 -10B +24 = 0

(B-6)(B-4) = 0

B= 6, and B=4

If B = 6, then A =4

Your two numbers are 6 and 4.

(B + A)/AB = 5/12