Question
Simplify. \( \frac{\frac{10 x^{5}}{x-3}}{\frac{5 x^{4}}{x+3}} \)
Ask by Lane Bright. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{2x^{2}+6x}{x-3} \).
Solution
Calculate or simplify the expression \( \frac{\frac{10x^5}{x-3}}{\frac{5x^4}{x+3}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{10x^{5}}{x-3}}{\frac{5x^{4}}{x+3}}\)
- step1: Multiply by the reciprocal:
\(\frac{10x^{5}}{x-3}\times \frac{x+3}{5x^{4}}\)
- step2: Reduce the fraction:
\(\frac{2x}{x-3}\times \left(x+3\right)\)
- step3: Multiply the terms:
\(\frac{2x\left(x+3\right)}{x-3}\)
- step4: Multiply the terms:
\(\frac{2x^{2}+6x}{x-3}\)
The simplified form of the expression \( \frac{\frac{10x^5}{x-3}}{\frac{5x^4}{x+3}} \) is \( \frac{2x^{2}+6x}{x-3} \).
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{\frac{10 x^{5}}{x-3}}{\frac{5 x^{4}}{x+3}} \), we can rewrite it by multiplying by the reciprocal of the denominator: \[ \frac{10 x^{5}}{x-3} \times \frac{x+3}{5 x^{4}}. \] Now we can simplify this step by step: 1. Multiply the numerators and denominators: \[ \frac{10 x^{5} (x + 3)}{(x - 3)(5 x^{4})}. \] 2. Now simplify the fraction: \[ \frac{10 x^{5}}{5 x^{4}} = \frac{10}{5} \cdot \frac{x^{5}}{x^{4}} = 2x. \] 3. So, now we have: \[ \frac{2x (x + 3)}{(x - 3)}. \] Thus, the simplified expression is: \[ \frac{2x (x + 3)}{x - 3}. \]
