The numerator of a fraction is 
\[3\] less than its denominator.
A new fraction is formed when 
\[2\] is multiplied with the numerator and 
\[4\] is added to the denominator.
The sum of both the fractions is 
 
\[\dfrac{1}{2}\].
Let the denominator of the first fraction be 
\[x\].
Write an equation in 
\[x\].

Let the denominator of the first fraction be \( x \). Since the numerator is 3 less than the denominator, the numerator of the first fraction is \( x - 3 \). Therefore, the first fraction is:

\[
\frac{x - 3}{x}
\]

For the second fraction, the numerator is multiplied by 2, so the new numerator becomes \( 2(x - 3) \). The denominator of the second fraction has 4 added to it, so the new denominator becomes \( x + 4 \). The second fraction is:

\[
\frac{2(x - 3)}{x + 4}
\]

We are told that the sum of the two fractions is \( \frac{1}{2} \). Therefore, the equation becomes:

\[
\frac{x - 3}{x} + \frac{2(x - 3)}{x + 4} = \frac{1}{2}
\]

This is the equation in terms of \( x \).

Would you like details on how to solve this equation? Here are 5 related questions:

1. How do you solve a rational equation like this one?
2. Can you simplify the expressions further before solving?
3. What happens if the denominator \( x \) is a specific value?
4. Can this type of problem appear in algebraic fractions?
5. What is the significance of checking for restrictions on \( x \)?

**Tip:** When adding fractions, always find a common denominator first to combine them properly.

The numerator of a fraction is 3 less than its denominator. A new fraction is formed when 2 is multiplied with the numerator and 4 is added to the denominator. The sum of both the fractions is 1/2. Let the denominator of the first fraction be x. Write an equation in x.

Learn how to form and solve a rational equation involving fractions where the numerator is 3 less than the denominator. This problem involves key algebraic concepts and teaches how to solve equations by adding fractions with different denominators. Ideal for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation