Math Problem Statement

z/z²-1*e1/z+1

Solution

The expression you provided is:

zz21ez+1\frac{z}{z^2 - 1} \cdot \frac{e}{z + 1}

Let's simplify this step by step.

  1. Recognize that z21z^2 - 1 is a difference of squares, which can be factored as: z21=(z1)(z+1)z^2 - 1 = (z - 1)(z + 1)

  2. Now rewrite the expression: z(z1)(z+1)ez+1\frac{z}{(z - 1)(z + 1)} \cdot \frac{e}{z + 1}

  3. Multiply the two fractions: ze(z1)(z+1)(z+1)\frac{z \cdot e}{(z - 1)(z + 1)(z + 1)} =ze(z1)(z+1)2= \frac{ze}{(z - 1)(z + 1)^2}

So the simplified expression is: ze(z1)(z+1)2\frac{ze}{(z - 1)(z + 1)^2}

Would you like further details or have any questions?

Here are 5 related questions:

  1. How do you factor quadratic expressions like z21z^2 - 1?
  2. What are some common rules for simplifying algebraic fractions?
  3. How does multiplying fractions work in algebra?
  4. Can we further simplify if given specific values for zz?
  5. How does the difference of squares formula help in solving algebraic expressions?

Tip: Always look for factoring opportunities in expressions involving squares or cubes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Fractions
Difference of Squares

Formulas

Difference of squares: a^2 - b^2 = (a - b)(a + b)
Multiplying fractions: (a/b) * (c/d) = ac/bd

Theorems

Difference of squares formula

Suitable Grade Level

Grades 9-12