Problem solving involving rational equation

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

2. The sum of a number and 6 times its reciprocal is - 5. Find the number.

3. The reciprocal of the product of two consecutive intergers is 1/72.

4. The reciprocal of the product of two consecutive integers is 1/42

Question

Mathematics

Dakota Walter

2 October, 17:26

Problem solving involving rational equation

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

2. The sum of a number and 6 times its reciprocal is - 5. Find the number.

3. The reciprocal of the product of two consecutive intergers is 1/72.

4. The reciprocal of the product of two consecutive integers is 1/42

+5

Answers (1)

Know the Answer?

Emmalee Sellers · Answer 1

Step-by-step explanation:

1) 1/5 + 1/7 = 1*7/5*7 + 1*5/7*5

=7/35 + 5/35 = 7+5/35 = 12/35

2) Let the number be x

x + 6*1/x = - 5

x + 6/x = - 5

(x² + 6) / x = - 5

x² + 6 = - 5x

x² + 5x + 6 = 0

x² + 3x + 2x + 2*3 = 0

x (x+3) + 2 (x+3) = 0

(x+3) (x+2) = 0

x + 3 = 0 or x + 2 = 0

x = - 3 or x = - 2

the number is (-3) or (-2)