assuming q$$ \neq0 $$ simplify the following expression $$ q^3r^2 $$/$$ q^3+q^3 $$r$$ ^2 $$

To simplify the expression $\frac{q^3r^2}{q^3 + q^3r^2}$, let's proceed step by step.

Given:
\[
\frac{q^3r^2}{q^3 + q^3r^2}
\]

### Step 1: Factor the denominator
Factor out $ q^3 $ from the denominator:
\[
q^3 + q^3r^2 = q^3(1 + r^2)
\]

So, the expression becomes:
\[
\frac{q^3r^2}{q^3(1 + r^2)}
\]

### Step 2: Simplify by canceling common factors
Since $ q^3 $ is present in both the numerator and the denominator, we can cancel it out:
\[
\frac{r^2}{1 + r^2}
\]

Thus, the simplified expression is:
\[
\frac{r^2}{1 + r^2}
\]

Would you like more details or have any questions?

Here are five related questions:
1. What happens to the expression if $ r = 1 $?
2. How would the expression change if the original numerator was $ q^4r^3 $?
3. What if $ q = 0 $? How does it affect the expression?
4. Can you find the derivative of the simplified expression with respect to $ r $?
5. How does the expression behave as $ r $ approaches infinity?

**Tip:** Always look for common factors in the numerator and denominator when simplifying algebraic fractions.

Learn how to simplify the algebraic fraction q^3r^2 / (q^3 + q^3r^2) step-by-step. Understand the process of factoring and canceling common factors to simplify algebraic expressions. Suitable for students in Grades 7-9 studying algebra and fraction simplification.

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