Calculating Fraction Expression Value

This solution explains how to find the value of the given mathematical expression involving fractions.

Problem Statement

We need to evaluate the expression: $ \frac{3}{4} + \frac{1}{\left(1+\frac{3}{7}\right)} - \frac{3}{4} $

Step-by-Step Solution

Step 1: Simplify the Expression

Observe the expression. We have a term $\frac{3}{4}$ and a term $-\frac{3}{4}$. These two terms cancel each other out because they are opposites.

$ \left(\frac{3}{4} - \frac{3}{4}\right) + \frac{1}{\left(1+\frac{3}{7}\right)} $

This simplifies the expression to:

Step 2: Evaluate the Denominator

Now, let's calculate the value inside the parenthesis in the denominator:

To add these, we need a common denominator. We can write 1 as $\frac{7}{7}$.

Adding the numerators gives:

Step 3: Calculate the Final Value

Substitute the value of the denominator back into the simplified expression:

Dividing 1 by a fraction is the same as taking the reciprocal of the fraction.

Therefore, the value is:

Conclusion

The value of the expression $\frac{3}{4} + \frac{1}{\left(1+\frac{3}{7}\right)} - \frac{3}{4}$ is $\frac{7}{10}$.