Chapter 8: Q 8.52. (page 927)

Divide: $\frac{2 z^{2}}{z^{2} - 1} \div \frac{z^{3} - z^{2} + z}{z^{3} - 1}$ .

Short Answer

Expert verified

The required answer is $\frac{2 z (z^{2} + z + 1)}{(z + 1) (z^{2} - z + 1)}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{2 z^{2}}{z^{2} - 1} \div \frac{z^{3} - z^{2} + z}{z^{3} - 1}$

Step 2. Simplify the expression.

$\frac{2 z^{2}}{z^{2} - 1} \div \frac{z^{3} - z^{2} + z}{z^{3} - 1}$

Rewrite the division as the product of the first rational expression and the reciprocal of the second.

$\frac{2 z^{2}}{z^{2} - 1} \cdot \frac{z^{3} - 1}{z^{3} - z^{2} + z}$

Factor the numerators and denominators and then multiply.

$\frac{2 z^{2}}{(z + 1) (z - 1)} \cdot \frac{(z - 1) (z^{2} + z + 1)}{z (z^{2} - z + 1)} \frac{2 z^{2} (z - 1) (z^{2} + z + 1)}{z (z + 1) (z - 1) (z^{2} - z + 1)}$

Simplify by dividing out common factors.

$\frac{2 z (z^{2} + z + 1)}{(z + 1) (z^{2} - z + 1)}$

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Divide: $\frac{2 z^{2}}{z^{2} - 1} \div \frac{z^{3} - z^{2} + z}{z^{3} - 1}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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Divide:2z2z2-1÷z3-z2+zz3-1.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Theoretical and Mathematical Physics

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Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Divide: $\frac{2 z^{2}}{z^{2} - 1} \div \frac{z^{3} - z^{2} + z}{z^{3} - 1}$ .