A positive integer is 1 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(7,6), then find the two integers

The two integers are 2 and 3.

Step-by-step explanation:

Let the larger positive integer be 'x'.

Now given:

A positive integer is 1 less than another.

So Smaller integer will be =

We need to find the two integers.

Solution:

Now given:

If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is

So we can say that;

Now we will make the denominator common using LCM.

Now denominator are common so we will solve the numerator;

Using cross multiplication we get;

Now we will find the roots of the equation we get;

Now we will solve separately to find the value of x we get;

Now we get 2 values 1 in fraction and 1 integer but given the two numbers are positive integer hence we will discard the fraction value we get;

Larger number =

Smaller number =

Hence the two integers are 2 and 3.

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5