Problem:
25-x^2 6
------ * ---
12 5-x
What I got:
5-x
---
2
*PLease Check My Work.
No.
Factor the 25-x^2 into two factors. Then the 5-x in the denominator divides out.
So then is it:
5+x
---
2
yes.
12x12
To check if your calculation is correct, you can simply substitute a value for x and compare the result with your expected answer.
Let's substitute x = 12 into the expression:
\( \frac{{25 - x^2}}{{12}} \times \frac{6}{{5 - x}} \)
First, factorize the numerator \(25 - x^2\) using the difference of squares formula:
\( (5 + x)(5 - x) \)
Substituting x = 12:
\( (5 + 12)(5 - 12) = (17)(-7) = -119 \)
Now, let's evaluate the denominator \(5 - x\) with x = 12:
\( 5 - 12 = -7 \)
So, the expression becomes:
\( \frac{{-119}}{{12}} \times \frac{6}{{-7}} \)
Finally, performing the multiplication:
\( \frac{{-119}}{{12}} \times \frac{6}{{-7}} = -\frac{{119 \cdot 6}}{{12 \cdot -7}} = -\frac{{714}}{{-84}} = \frac{{119}}{{14}} \)
Therefore, your answer is incorrect. The correct answer is \( \frac{{119}}{{14}} \), not \( \frac{{5 + x}}{{2}} \)