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in which case the given value is equal to 1 and the given numbers are not returned

The equation given in the image is:

\[
\frac{1}{a} + \frac{2}{b} + \frac{f}{c + d} + \frac{f}{g + h} = 1
\]

The variables provided are:
\[
a, b, c, d, e, f, g, h = 2, 3, 4, 5, 6, 7, 8, 9
\]

We need to substitute the given values into the equation and check when the result equals 1.

Let's proceed step by step to see if the equation holds true when the provided values are substituted.

The values are:
- \( a = 2 \)
- \( b = 3 \)
- \( c = 4 \)
- \( d = 5 \)
- \( f = 7 \)
- \( g = 8 \)
- \( h = 9 \)

Substitute these into the equation and calculate:

\[
\frac{1}{2} + \frac{2}{3} + \frac{7}{4 + 5} + \frac{7}{8 + 9} = 1
\]

Now, simplify each term.

1. \(\frac{1}{2} = 0.5\)
2. \(\frac{2}{3} \approx 0.6667\)
3. \(4 + 5 = 9\), so \(\frac{7}{9} \approx 0.7778\)
4. \(8 + 9 = 17\), so \(\frac{7}{17} \approx 0.4118\)

Now sum them up:

\[
0.5 + 0.6667 + 0.7778 + 0.4118 = 2.3563
\]

The sum is approximately 2.3563, which is not equal to 1. Thus, using the provided values for \(a, b, c, d, f, g,\) and \(h\), the equation does not result in 1.

### Would you like to explore further or try different values? Here are some possible next steps:
1. Can we adjust the values to make the equation equal to 1?
2. What happens if we change only one variable at a time?
3. What if \(f\) or another variable takes a different value, does it balance the equation?
4. Is there an alternative approach or form for this equation?
5. Should we rearrange the equation or apply any specific mathematical strategy?

**Tip:** When dealing with fractions, consider simplifying each part before summing to avoid rounding errors!

In which case is the given equation equal to 1 and the given numbers do not result in this value?

Explore how to solve the fractional equation (1/a) + (2/b) + (f/(c + d)) + (f/(g + h)) = 1 using provided values. This detailed explanation breaks down the process for algebra students in Grades 7-10, showing that the sum does not equal 1 and discussing further potential explorations.

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