Let’s simplify this expression step by step.
We are given:
\[
\frac{\frac{3}{x^2 + 5x}}{\frac{-2x}{(x+5)x} + \frac{1(x+5)}{(x+5)x}}
\]
Wait — looking at the image, it seems like the denominator is being rewritten as a single fraction. Let me rewrite the original problem clearly based on what’s shown:
Original expression to simplify:
\[
\frac{\frac{3}{x^2 + 5x}}{\frac{-2x}{x(x+5)} + \frac{1(x+5)}{x(x+5)}}
\]
Note: \( x^2 + 5x = x(x+5) \), so we can use that to help us.
---
Step 1: Simplify the denominator.
The denominator is:
\[
\frac{-2x}{x(x+5)} + \frac{1(x+5)}{x(x+5)}
\]
Since both fractions have the same denominator, we can combine them:
\[
= \frac{-2x + (x+5)}{x(x+5)}
\]
Now simplify the numerator of that fraction:
\[
-2x + x + 5 = -x + 5
\]
So the entire denominator becomes:
\[
\frac{-x + 5}{x(x+5)}
\]
---
Step 2: Now go back to the whole expression.
We now have:
\[
\frac{\frac{3}{x(x+5)}}{\frac{-x + 5}{x(x+5)}}
\]
Dividing two fractions means multiplying by the reciprocal:
\[
= \frac{3}{x(x+5)} \cdot \frac{x(x+5)}{-x + 5}
\]
---
Step 3: Cancel common factors.
Notice that \( x(x+5) \) appears in both numerator and denominator — they cancel out!
So we’re left with:
\[
\frac{3}{-x + 5}
\]
Which can also be written as:
\[
\frac{3}{5 - x}
\]
(because \(-x + 5 = 5 - x\))
---
Final Answer:
\[
\boxed{\frac{3}{5 - x}}
\]
Parent Tip: Review the logic above to help your child master the concept of complex fraction.
