Answer:

[tex]\frac{1}{7} + \frac{1}{8} = \frac{15}{56}[/tex]

Step-by-step explanation:

Let the two consecutive numbers be x and x+1.

Then the reciprocal of two consecutive numbers x and x+1 would be 1/x and 1/(x+1) respectively.

According to the problem given:

[tex]\frac{1}{x} + \frac{1}{x+1} = \frac{15}{56}[/tex].

Now, we have to solve for the value of x.

[tex]\frac{1}{x} + \frac{1}{x+1} = \frac{15}{56}\\\frac{(x+1)+x}{x(x+1)} = \frac{15}{56}\\(2x+1)(56) = 15(x^{2} +x)\\112x+56 = 15x^{2} + 15x\\15x^{2} + 15x - 112x - 56 = 0\\15x^{2} -97x - 56 = 0[/tex]

Solving the equation we would get two values of x = 7 and x =  -8/15.

Hence, 7 and 8 i.e. x, x+1 are the two consecutive numbers that we have to find.

[tex]\frac{1}{7} + \frac{1}{8} = \frac{15}{56}[/tex]