Textbook Question
Find the domain of each rational expression. 12/ (x2 + 5x + 6)
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0. Review of Algebra
Exponents
2:18 minutesProblem 33a
Textbook Question
Multiply or divide, as indicated. 15p3/9p2 * 12p/10p3
Verified step by step guidance1
Start by writing the entire expression as a single fraction multiplication: \(\frac{15p^3}{9p^2} \times \frac{12p}{10p^3}\).
Combine the numerators and denominators into one fraction: \(\frac{15p^3 \times 12p}{9p^2 \times 10p^3}\).
Multiply the coefficients (numbers) in the numerator and denominator separately: numerator is \(15 \times 12\), denominator is \(9 \times 10\).
Apply the laws of exponents to multiply powers of \(p\): when multiplying like bases, add the exponents. So in the numerator, \(p^3 \times p^1 = p^{3+1} = p^4\), and in the denominator, \(p^2 \times p^3 = p^{2+3} = p^5\).
Simplify the fraction by reducing the coefficients to lowest terms and subtract the exponents of \(p\) in numerator and denominator (since \(\frac{p^a}{p^b} = p^{a-b}\)).
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2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Multiplication and Division of Algebraic Fractions
When multiplying or dividing algebraic fractions, multiply or divide the numerators together and the denominators together. Simplify the resulting fraction by factoring and reducing common factors to make the expression simpler.
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