Question
tor the fractions in the equation \( \frac{7}{x-2}=\frac{2}{(x-2)} \)
Ask by Moreno Long. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There is no solution to the equation.
Solution
It appears you want to solve the equation:
\[
\frac{7}{x - 2} = \frac{2}{x - 2}
\]
Let's solve for \( x \):
1. **Identify the Equation:**
\[
\frac{7}{x - 2} = \frac{2}{x - 2}
\]
2. **Check the Denominator:**
First, note that \( x - 2 \) cannot be zero because division by zero is undefined. Therefore:
\[
x - 2 \neq 0 \implies x \neq 2
\]
3. **Simplify the Equation:**
Since both sides of the equation have the same denominator and the denominators are not zero, we can equate the numerators:
\[
7 = 2
\]
4. **Analyze the Result:**
The statement \( 7 = 2 \) is **false**. This means there is no value of \( x \) (other than the excluded value \( x = 2 \)) that satisfies the original equation.
5. **Conclusion:**
**There is no solution** to the equation.
\[
\boxed{\text{No solution}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the equation \( \frac{7}{x-2}=\frac{2}{x-2} \), you can start by noticing that both sides of the equation have a common denominator, \(x-2\). For simplicity, we can multiply both sides by \(x-2\) (as long as \(x \neq 2\) to avoid division by zero). This gives us: \[ 7 = 2. \] This is a contradiction, which means there is no solution to the equation. The fractions lead us to realize that the only value for \(x\) that would make the original equation undefined is \(x = 2\). Thus, the equation has no solutions. If you need any further help, just let me know!
