Multiply and simplify: (2/x) * (3x/10) * (x^2/12) plus (10/x) , (12/5x^2)
Understand the Problem
The question appears to involve multiplying and simplifying algebraic fractions. You are asked to multiply the given fractions and then simplify the result to its lowest terms.
Answer
1. $\frac{x^2}{20}$ 2. $\frac{24}{x^3}$
Answer for screen readers
- $\frac{x^2}{20}$
- $\frac{24}{x^3}$
Steps to Solve
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Multiply the first set of fractions Multiply the numerators and the denominators of the first set of fractions: $\frac{2}{x} \cdot \frac{3x}{10} \cdot \frac{x^2}{12}$. $$ \frac{2 \cdot 3x \cdot x^2}{x \cdot 10 \cdot 12} = \frac{6x^3}{120x} $$
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Simplify the resulting fraction Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. In this case, we can divide both by $6x$: $$ \frac{6x^3}{120x} = \frac{6x \cdot x^2}{6x \cdot 20} = \frac{x^2}{20} $$
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Multiply the second set of fractions Multiply the numerators and the denominators of the second set of fractions: $\frac{10}{x} \cdot \frac{12}{5x^2}$. $$ \frac{10 \cdot 12}{x \cdot 5x^2} = \frac{120}{5x^3} $$
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Simplify the resulting fraction Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. In this case, we can divide both by $5$: $$ \frac{120}{5x^3} = \frac{5 \cdot 24}{5 \cdot x^3} = \frac{24}{x^3} $$
- $\frac{x^2}{20}$
- $\frac{24}{x^3}$
More Information
Simplifying algebraic fractions involves multiplying the fractions as usual, and then canceling out common factors from the numerator and denominator. This usually involves numbers and variables (in this case $x$).
Tips
- Forgetting to multiply all numerators and denominators together.
- Incorrectly simplifying the fraction, such as not finding the greatest common factor.
- Making arithmetic errors during multiplication or simplification.
- Not simplifying the expression completely.
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