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K Perform the indicated operation. h³-1 h4-1 6h² +6h+6 h³ +h² +h+1 ..

K Perform the indicated operation. h³-1 h4-1 6h² +6h+6 h³ +h² +h+1 ..

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Rational expression

**Perform the Indicated Operation** Given the expression: \[ \frac{\frac{h^3 - 1}{h^4 - 1}}{\frac{6h^2 + 6h + 6}{h^3 + h^2 + h + 1}} \] Simplify the expression by performing the indicated operations. 1. **Identify the Numerator and Denominator:** - Numerator: \(\frac{h^3 - 1}{h^4 - 1}\) - Denominator: \(\frac{6h^2 + 6h + 6}{h^3 + h^2 + h + 1}\) 2. **Operation:** - The expression can be simplified by multiplying the numerator by the reciprocal of the denominator: \[ \left(\frac{h^3 - 1}{h^4 - 1}\right) \times \left(\frac{h^3 + h^2 + h + 1}{6h^2 + 6h + 6}\right) \] 3. **Required Result:** - Find the simplified fraction or integer that represents the product above. 4. **Input Area:** - The expression equals \(\Box\). (Type an integer or a simplified fraction.) Please solve this operation following algebraic rules to find the correct simplified answer.
Transcribed Image Text:**Perform the Indicated Operation** Given the expression: \[ \frac{\frac{h^3 - 1}{h^4 - 1}}{\frac{6h^2 + 6h + 6}{h^3 + h^2 + h + 1}} \] Simplify the expression by performing the indicated operations. 1. **Identify the Numerator and Denominator:** - Numerator: \(\frac{h^3 - 1}{h^4 - 1}\) - Denominator: \(\frac{6h^2 + 6h + 6}{h^3 + h^2 + h + 1}\) 2. **Operation:** - The expression can be simplified by multiplying the numerator by the reciprocal of the denominator: \[ \left(\frac{h^3 - 1}{h^4 - 1}\right) \times \left(\frac{h^3 + h^2 + h + 1}{6h^2 + 6h + 6}\right) \] 3. **Required Result:** - Find the simplified fraction or integer that represents the product above. 4. **Input Area:** - The expression equals \(\Box\). (Type an integer or a simplified fraction.) Please solve this operation following algebraic rules to find the correct simplified answer.
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\large \frac{\frac{h^3-1}{h^4-1}}{\frac{6h^2+6h+6}{h^3+h^2+h+1}}

use the fraction rule \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}

=\frac{\left(h^3-1\right)\left(h^3+h^2+h+1\right)}{\left(h^4-1\right)\left(6h^2+6h+6\right)}

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