Hon Alg 2: 9.1-9.2 Review

How do we find the restrictions of a rational expression?

• We set the numerator equal to zero and solve for the variable

• We set the denominator equal to zero and solve for the variable

• We plug zero into the numerator and simplify

• We plug zero into the denominator and simplify

What are the restrictions of:    $\frac{c-5}{c+5}$  

•  $c\ne5$  

•  $c\ne-5$  

•  $c\ne5$  and  $c\ne-5$  

• (-5, 0)
  

Write this product in simplest form:
  $\frac{6a^2b}{15c^3}\cdot\frac{5c}{4a}$  

•  $\frac{30a^2bc}{60ac^3}$  

•  $\frac{a^2bc}{2ac^3}$  

•  $\frac{30a^2bc}{60ac^3}$  

•  $\frac{ab}{2c^2}$  

What are the restrictions of:    $\frac{8x}{\left(x+4\right)\left(x-5\right)}$  

(Pick all that apply!)

•  $x\ne5$  

•  $x\ne-5$  

•  $x\ne0$  

•  $x\ne4$  

•  $x\ne-4$  

What are the restrictions of:   $\frac{19}{8u\left(u+2\right)}$  

(Pick all that apply!)

•  $u\ \ne0$  

•  $u\ \ne2$  

•  $u\ \ne-2$  

•  $u\ne8$  

•  $u\ne-8$  

Student 1 says that the restrictions of $\frac{9\left(d-4\right)}{\left(d-7\right)\left(d+8\right)}$ are $d\ne4$ , $d\ne7$ , and $d\ne-8$ . Is Student 1 correct? Why?

• Yes because d = 4, d = 7, and d = -8 all make the denominator equal to zero

• Yes because d = 4, d = 7, and d = -8 all make the expression evaluate to zero

• No because d = 4 does not make the denominator equal to zero

• No because the real restrictions are $d\ne-4$ , $d\ne-7$ , and $d\ne8$

• No because d = 0 is also a restriction

What are the restrictions of: $\frac{1}{5y\ -\ 4}$

• $y\ne4$

• $y\ \ne-4$

• $y\ \ne5$

• $y\ \ne-5$

• $y\ \ne\frac{4}{5}$

Find the quotient: $\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}$  

•  $\frac{5a\left(a+4\right)}{3}$  

•  $\frac{a^3-2a^2-4a+8}{15a^3}$  

•  $\frac{5a^2+20a}{3}$  

•  $\frac{a^3-6a+8}{15a}$  

Simplify: $\frac{\frac{m^2-4n^2}{m+2n}}{\frac{1}{m+2n}}$  

•  $\frac{m^2-4n^2}{m^2+4mn+n^2}$  

•  $\frac{m-2n}{m+2n}$  

•  $\frac{m+2n}{m-2n}$  

•  $m^2-4n^2$  

Subtract: $\frac{9x+1}{x-2}-\frac{3x-4}{x-2}$  

•  $\frac{6x-3}{x-2}$  

•  $\frac{12x+5}{x-2}$  

•  $\frac{6x+5}{x-2}$  

•  $\frac{12x-3}{x-2}$