8.1 Rational Expressions

 $\frac{x^2-1}{4-x^2}\cdot\frac{x^2-5x-14}{x^2-6x-7}$  
completely simplify the above

•  $\frac{x-1}{x-2}$  

•  $-\frac{x-1}{x-2}$  

•  $\frac{\left(x-1\right)\left(x+2\right)}{–x^2+4}$  

•  $\frac{x-2}{x+1}$  

• None of these are correct.

Tags

CCSS.HSA.APR.D.6

 $\frac{2x^2+7x-4}{8x^2-4x}\div\frac{-5x-20}{4x}$  

•  $\frac{1}{5}$  

•  $-5$  

•  $\frac{2x-1}{x+4}$  

•  $\frac{2x-1}{5}$  

• None of these are correct

Tags

CCSS.HSA.APR.D.6

 $\frac{r^2+5r}{2r}\div\frac{r^2-25}{6r-12}$  

Completely simplify the above

•  $\frac{3\left(r-2\right)}{r-5}$  

•  $\frac{5}{3r-12}$  

•  $\frac{6r-12}{2r\left(r+5\right)}$  

•  $\frac{r-2}{r-5}$  

• None of these are correct.

Tags

CCSS.HSA.APR.D.6

 $\frac{\frac{x^2+3x-18}{x+4}}{\frac{x^2+7x+6}{x+4}}$  
completely simplify the above

•  $\frac{x-3}{x+1}$  

•  $\frac{x+3}{x-1}$  

•  $\frac{x+1}{x-3}$  

•  $\frac{x-1}{x+3}$  

• None of these are correct

Tags

CCSS.HSA.APR.D.6

 $\frac{x^2}{2x}-\frac{5}{2x}$  
simplify the above

•  $x-5$  

•  $\frac{x^2-5}{2x}$  

•  $\frac{x-5}{2}$  

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

• None of these are correct

Tags

CCSS.HSA.APR.D.7

 $\frac{8}{y-3}+\frac{2y-5}{y^2-12y+27}$  

•  $\frac{2y+3}{\left(y-3\right)\left(y-9\right)}$  

•  $\frac{10y-7}{\left(y-3\right)\left(y+9\right)}$  

•  $\frac{10y-77}{\left(y-9\right)\left(y-3\right)}$  

•  $\frac{10\left(y-7\right)}{\left(y-3\right)\left(y-9\right)}$  

•  None of these are correct

Tags

CCSS.HSA.APR.D.7

Add
 $\frac{3x-2}{x+2}+\frac{2x}{4x-1}$  

•  $\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$  

•  $\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1$  

•  $\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$  

•  $\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2$  

Tags

CCSS.HSA.APR.D.7

Subtract
 $\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$  

Tags

CCSS.HSA.APR.D.7