Multiplying and Dividing Rational Expressions

 $\frac{b^2+2b-63}{b+9}\div\frac{b^2+2b-63}{b^2-13b+42}$  

Simplify and state the restrictions on the domain.

•  $\frac{\left(b-6\right)\left(b-7\right)}{b+9};\ \ \ b\ne-9,\ 7,\ 6$  

•  $\frac{b+2}{b-7}\ \ \ \ \ x\ne7$  

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

•  $\frac{14}{b+2}\ \ \ \ \ \ x\ne-2$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify and state the restrictions on the domain

 $\frac{10x-60}{x^2-36}\div\frac{4x-20}{x+6}$  

•  $\frac{2x}{7\left(x+8\right)}\ \ \ \ \ \ \ \ x\ne-8$  

•  $\frac{2}{x}\ \ \ \ \ \ \ x\ne0$  

•  $\frac{5}{2\left(x-5\right)}\ \ \ \ \ \ \ \ \ \ \ x\ne6,\ -6,\ 5$  

•  $\frac{x-2}{14}\ \ \ \ \ \ \ none$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Simplify and state the restrictions on the domain.

 $\frac{n^2+6n+5}{n^2+13n+36}\ \cdot\ \frac{3n+27}{3n+15}$  

•  $\frac{n+1}{n+4}\ \ \ \ \ \ \ \ \ n\ne-9,\ -4,\ -5$  

•  $\frac{90n^3}{n+5}\ \ \ \ \ \ \ \ \ \ \ n\ne-5$  

•  $\frac{49n^2}{n-3}\ \ \ \ \ \ \ n\ne3$  

•  $3\ \ \ \ n\ne0$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{7a^2-35a}{8a^3-40a^2}\ \cdot\ \frac{8a^3+40a^2}{a+5}$  

Simplify and state the restrictions on the domain.

•  $\frac{a+7}{6\left(a-6\right)}\ \ \ \ \ \ \ a\ne6$  

•  $5\ \ \ \ \ \ none$  

•  $7a\ \ \ \ \ \ a\ne0,\ 5,\ -5$  

•  $\frac{a+7}{a-4}\ \ \ \ \ \ \ \ \ a\ne4$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{5x-30}{5}\ \cdot\ \frac{x^2+2x-48}{x^2-12x+36}$  

Simplify and state the restrictions on the domain.

•  $\frac{x-1}{6x^2}\ \ \ \ \ \ \ x\ne0$  

•  $x+8\ \ \ \ \ \ \ \ \ \ \ x\ne6$  

•  $14x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ none$  

•  $\frac{\left(x-7\right)\left(x-4\right)}{x-8}\ \ \ \ \ \ \ \ \ \ x\ne8$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{x-2}{x^2-12x+20}\ \div\ \frac{x^2+3x-70}{10x-100}$  

Simplify and state the restrictions on the domain.

•  $\frac{9}{8}\ \ \ \ \ \ \ none$  

•  $\frac{x-6}{6x^2}\ \ \ \ \ \ \ \ \ x\ne0$  

•  $\frac{10\left(x-8\right)}{x-9}\ \ \ \ \ \ \ x\ne9$  

•  $\frac{10}{\left(x-7\right)\left(x+10\right)}\ \ \ \ \ \ \ \ \ \ x\ne10,\ 2,\ 7,\ -10$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{p^2+7p-8}{p^2-p-42}\ \div\ \frac{p-4}{p^2-11+28}$  

Simplify and state the restrictions on the domain.

•  $\frac{\left(p-1\right)\left(p+8\right)}{p+6}\ \ \ \ \ \ \ \ \ \ \ \ p\ne7,\ -6,\ 4$  

•  $\frac{p-7}{5}\ \ \ \ \ \ \ none$  

•  $\frac{2\left(p-10\right)}{p-3}\ \ \ \ \ \ \ \ \ \ p\ne3$  

•  $\frac{5\left(p-4\right)}{7p}\ \ \ \ \ \ \ \ \ \ \ \ p\ne0$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{8m^2+64m}{m^2-m-72}\ \cdot\ \frac{20m^2+4m}{40m^2+8m}$  

Simplify and state the restrictions on the domain.

•  $m-6\ \ \ \ \ \ \ m\ne9$  

•  $\frac{4m}{m-9}\ \ \ \ \ \ \ \ \ \ \ m\ne9,\ -8,\ 0,\ -\frac{1}{5}$  

•  $42m^3\ \ \ \ \ \ \ \ \ m\ne9,\ -8,\ 0,\ -\frac{1}{5}$  

•  $\frac{4m}{m-7}\ \ \ \ \ \ \ \ \ \ m\ne7$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{x^2-8x+15}{x-9}\ \cdot\ \frac{3x^2+27x}{x^2+6x-27}$  

Simplify and state the restrictions on the domain.

•  $\frac{2}{p+1}\ \ \ \ \ \ \ \ \ p\ne-1$  

•  $\frac{5}{2}\ \ \ \ \ \ \ \ p\ne3$  

•  $\frac{3p\left(p-5\right)}{p-9}\ \ \ \ \ \ p\ne9,\ 3,\ -9$  

•  $9p^2\ \ \ \ \ non$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{x^2+5x-36}{x^2-7x-30}\ \cdot\ \frac{x^2-7x-30}{10x^3+90x^2}$  

Simplify and state the restrictions on the domain.

•  $\frac{\left(x+8\right)\left(x-1\right)}{x-7}\ \ \ \ \ \ \ \ \ \ \ x\ne7$  

•  $\frac{x-4}{10x^2}\ \ \ \ \ \ \ \ \ x\ne10,\ -3,\ 0,\ 9$  

•  $\frac{9\left(x+9\right)}{10}\ \ \ \ \ \ \ \ \ \ x\ne10,\ -3,\ 0,\ -9$  

•  $x-1\ \ \ \ \ \ x\ne10,\ -3,\ 0,\ -9$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.7