Question

Express in simplest form: x2−49/7x−x2 (1 point) Responses x+7x the fraction with numerator x plus 7 and denominator x −(x+7)x the fraction with numerator negative open paren x plus 7 close paren and denominator x −7x negative 7 over x -7 -7

Answer 1

To simplify the expression \(\frac{x^2 - 49}{7x - x^2}\), we begin by factoring both the numerator and the denominator.

1. **Factor the numerator** \(x^2 - 49\):
- Notice that this is a difference of squares:
\[
x^2 - 49 = (x - 7)(x + 7)
\]

2. **Factor the denominator** \(7x - x^2\):
- We can factor out a negative sign and rearrange:
\[
7x - x^2 = - (x^2 - 7x) = - (x(x - 7))
\]

Now rewriting the entire expression using these factors gives us:
\[
\frac{(x - 7)(x + 7)}{-(x(x - 7))}
\]

3. **Cancel the common factor** \(x - 7\):
- Since \(x \neq 7\) to avoid division by zero, we can cancel out the \(x - 7\) from the numerator and denominator:
\[
\frac{(x + 7)}{-x}
\]

4. **Rewriting the simplified expression**:
\[
-\frac{x + 7}{x}
\]

This can be expressed as:
\[
-\frac{x}{x} - \frac{7}{x} = -1 - \frac{7}{x}
\]

So, the simplest form of the expression is:
\[
-\frac{x + 7}{x}
\]

Thus, your answer is:
\[
-(x + 7)/x
\]

**In standard notation**: The fraction with numerator \(- (x + 7)\) and denominator \(x\).