Rational Arithmetic

Rewrite each polynomial in factored form:

• $\frac{\left(x-6\right)\left(x+6\right)}{3\left(x+6\right)}\div\frac{\left(x+7\right)\left(x-6\right)}{3x^2}$

• $\frac{x^2-12}{x+6}\div\frac{\left(x-7\right)\left(x-6\right)}{3x^2}$

• $\frac{\left(x-6\right)\left(x+6\right)}{x+6}\div\frac{\left(x+7\right)\left(x-6\right)}{x^2}$

• $\frac{\left(x+6\right)^2}{3\left(x+6\right)}\div\frac{\left(x+7\right)\left(x-6\right)}{x^2}$

Simplify:

•  $\frac{x^2}{x+7}$ 

•  $\frac{\left(x+7\right)\left(x-6\right)}{3\left(x+6\right)}$ 

•  $\frac{x^2}{3\left(x+7\right)}$ 

•  $\frac{9\left(x+7\right)}{x^2}$ 

Rewrite each polynomial in factored form:

• $\frac{4\left(x-8\right)\left(x-2\right)}{x^2\left(x-6\right)}\cdot\frac{\left(x-6\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}$

• $\frac{\left(4x-4\right)\left(x-2\right)}{x^2\left(x-6\right)}\cdot\frac{\left(x+6\right)\left(x+3\right)}{\left(x-2\right)\left(x-3\right)}$

• $\frac{4\left(x-8\right)\left(x-2\right)}{x^2\left(x+6\right)}\cdot\frac{\left(x-6\right)\left(x-3\right)}{\left(x+2\right)\left(x+3\right)}$

• $\frac{4\left(x-8\right)\left(x-2\right)}{x^2-6}\cdot\frac{\left(x-6\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}$

Simplify:

•  $\frac{4x-32}{x^2}$ 

•  $\frac{4\left(x-8\right)}{x^2}$ 

•  $\frac{x^2}{x-8}$ 

•  $\frac{x^2}{4\left(x-6\right)}$   $\$ 

Rewrite each polynomial in factored form:

• $\frac{9}{\left(x-9\right)\left(x-5\right)}\cdot\frac{\left(x-5\right)}{\left(x+9\right)}\div\frac{4x}{9x\left(x-9\right)\left(x+9\right)}$

• $\frac{9}{\left(x+9\right)\left(x+5\right)}\cdot\frac{\left(x-5\right)}{\left(x+9\right)}\div\frac{4}{9x^2\left(x-9\right)\left(x+9\right)}$

• $\frac{9}{\left(x-9\right)\left(x-5\right)}\cdot\frac{\left(x-5\right)}{\left(x+9\right)}\div\frac{4x}{9x\left(x-9\right)^2}$

• $\frac{1}{x\left(x-5\right)}\cdot\frac{\left(x-5\right)}{\left(x+9\right)}\div\frac{4x}{9x\left(x-9\right)\left(x+9\right)}$

Simplify:

•  $\frac{81}{4}$ 

•  $\frac{9\left(x-9\right)}{4}$ 

•  $\frac{9x-81}{4}$  

•  $4$  

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What is the least common denominator?

What is the least common denominator?

What is the least common denominator?