Algebra Problem No.7

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@ Mr. Eric | Monday, Aug 16, 2021 | 1 minute read | Update at Monday, Aug 16, 2021

Complete each problem below by hand. Show your work and provide a reason for each step. Calculators or other graphing devices are not allowed on this assignment.

  1. Simplify the following complex fraction to linear factors.

$$ \dfrac{\frac{6}{x^2+2x-15}-\frac{1}{x-3}}{\frac{1}{x+5}+1} $$

What are the key points of this function? When is this function positive?

Answer

Oops … missing question “When is this function positive”

Answer

  1. Solve the rational inquality

$$ \dfrac{x^2-3x-2}{x^2+5x+6}>\dfrac{2-x}{x^2-4} $$

Answer

  1. Consider the rational function

$$ f(x)=\dfrac{x^2+8x+15}{x^4+8x^3+14x^2-8x-15} $$

Notice the denominator is the same as your work on Algebra Problem: Chapter 4. Use your previous results to:

a. Find all zeros of $f(x)$.

Answer

b. Find the asymptotes.

Answer

c. Sketch a graph $f(x)$ including all key features previously found. Include how you graphed.

Answer

Answer

Answer

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