Reviewing Simplifying Rational Expressions by Factoring

Reviewing Simplifying Rational Expressions by Factoring

First, we will review how to simplify rational expressions by factoring, then you will be assessed on this material!

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TO SUMMARIZE

Factor numerator & denominator

List the excluded values

Cancel common factors

Multiple Choice

Factor:

$$x^2-7x+10$$  

• $$\left(x+5\right)\left(x+2\right)$$  

• $$\left(x-5\right)\left(x+2\right)$$  

• $$\left(x-5\right)\left(x-2\right)$$  

• $$\left(x+5\right)\left(x-2\right)$$  

Multiple Choice

Factor:

$$4x^2-9$$  

• $$\left(2x+3\right)\left(2x-3\right)$$  

• $$\left(2x+3\right)\left(2x+3\right)$$  

• $$\left(2x-3\right)\left(2x-3\right)$$  

• $$\left(4x+9\right)\left(4x-9\right)$$  

Multiple Choice

Factor completely:

$$2x^2-8x$$  

• $$2x\left(x-4\right)$$  

• Not Factorable

• $$2x\left(2x-8\right)$$  

• $$2\left(x^2-4x\right)$$  

Multiple Choice

What are the excluded values for

$$\frac{\left(x+3\right)}{\left(x+2\right)\left(x+1\right)}$$  

• $$x\ne2,\ x\ne1$$  

• $$x\ \ne\ -2,\ x\ \ne\ -1$$  

• $$x\ne-2,\ x\ne-1,\ x\ne-3$$  

• $$x\ne2,\ x\ne1,\ x\ne3$$  

Multiple Choice

What expression is equivalent to  $$\frac{\left(x-5\right)}{\left(x-5\right)\left(x-4\right)}$$  

• $$\frac{1}{x-4}$$

• $$x-4$$

• $$\frac{1}{-9x-4}$$

• $$-9x-4$$

Multiple Choice

What is the simplified version of $$\frac{\left(x+4\right)\left(x+1\right)}{\left(x-5\right)\left(x+1\right)}$$

• $$\frac{x+4}{x+1}$$

• $$x+1$$

• $$\frac{x+4}{x-5}$$

• $$\frac{x+1}{x-5}$$

Multiple Choice

What is the correct factored form? $$\frac{x^2+5x+4}{x^{2\ }-4x-5}$$

• Factor:

  $$\frac{\left(x+1\right)\left(x+4\right)}{\left(x-5\right)\left(x+1\right)}$$

• Factor:

  $$\frac{\left(x+2\right)\left(x+2\right)}{\left(x-5\right)\left(x-1\right)}$$

• Factor:

  $$\frac{\left(x+2\right)\left(x-2\right)}{\left(x+5\right)\left(x-5\right)}$$

• Factor:

  $$\frac{\left(x-4\right)\left(x-1\right)}{\left(x+5\right)\left(x-1\right)}$$

Multiple Select

Choose every excluded value for $$\frac{\left(x+4\right)\left(x+1\right)}{\left(x-5\right)\left(x+1\right)}$$

• $$x\ne1$$

• $$x\ne5$$

• $$x\ne-1$$

• $$x\ne-5$$

Multiple Choice

What is the simplified version of $$\frac{\left(x+4\right)\left(x+1\right)}{\left(x-5\right)\left(x+4\right)}$$

• $$\frac{x+4}{x+1}$$

• $$x+1$$

• $$\frac{x+4}{x-5}$$

• $$\frac{x+1}{x-5}$$

Multiple Choice

What is the correct factored form? $$\frac{x^2+5x}{x^{2\ }-25}$$

• Factor:

  $$\frac{x\left(x+5\right)}{\left(x-5\right)\left(x-5\right)}$$

• Factor:

  $$\frac{\left(x+5\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}$$

• Factor:

  $$\frac{x\left(x+5\right)}{\left(x+5\right)\left(x+5\right)}$$

• Factor:

  $$\frac{x\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$$

Multiple Select

Choose every excluded value for $$\frac{x\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$$

• $$x\ne-5$$

• $$x\ne5$$

• $$x\ne0$$

• $$x\ne1$$

Multiple Choice

What is the simplified version of $$\frac{x\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$$

• $$\frac{1}{x-5}$$

• $$x-5$$

• $$x$$

• $$\frac{x}{x-5}$$