Operations with Rational Expressions

Operations with Rational Expressions

​Dr. Tom Giles

Operations with Rational Expressions

Multiple Choice

We Do

Multiple Choice

You Do

Multiple Choice

We Do: Find the LCD of the following rational expressions
$$\frac{2x}{x+1}$$  and  $$\frac{1}{x^2-1}$$

• (x+1)(x-1)

• (x+1)² (x-1)

• (2x+2)

Multiple Choice

I Do: 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

Multiple Choice

We Do: Since we know that the denominator cannot equal, what are the restrictions of the rational expression? $$\frac{5x}{x^2-16}$$  

• $$x\ne\pm16$$  

• $$x\ne-4$$  

• $$x\ne\pm4$$  

• $$x\ne4$$  

Multiple Choice

We Do: Add

$$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$$  

• $$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$$  

• $$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$$  

• $$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$$  

• $$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$$  

Multiple Choice

You Do: Add

$$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$$  

• $$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

• $$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$$  

• $$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

• $$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

Multiple Choice

You Do: Subtract

$$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$$  

• $$\frac{x^2-2x-8}{2x+7}\ ,\ x\ne-\frac{7}{2}$$

• $$x^2-2x-8\ ,\ x\ne0$$  

• $$x^2-2x+2\ ,\ x\ne0$$  

• $$\frac{x^2-2x+2}{2x+7}\ ,\ \ x\ne-\frac{7}{2}$$  

Multiple Choice

Subtract

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

• $$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{2}{3}$$  

• $$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{3}{2}$$  

• $$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{3}{2}$$  

• $$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{2}{3}$$  

Multiple Choice

You Do: Subtract

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

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

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

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

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

Multiple Choice

You Do: Multiply the following rational expression:
$$\frac{8x}{3x^2y^2}\ \times\frac{9x^2y}{4a}=$$  

• $$\frac{6x}{ay}$$  

• $$\frac{6}{a}$$  

• $$\frac{9x}{y}$$  

• $$\frac{6x}{9y}$$  

Multiple Choice

We Do:

• $$\frac{7(r+2)}{r+2}$$

• $$\frac{r-8}{r+2}$$

• $$\frac{r+2}{7}$$
  

• $$\frac{r-8}{7}$$
  

Multiple Choice

You Do: Simplify.

• A

• B

• C

• D

Multiple Choice

You Do: Multiply and Simplify

• $$\frac{4(x+3)}{x+2}$$

• $$\frac{x+2}{4(x+1)}$$
  

• $$\frac{x+2}{4(x+3)}$$
  

• $$\frac{4(x+1)}{x+2}$$
  

Multiple Choice

We Do: Find the equivalent expression for  $$\frac{4}{7}\div\frac{7}{1}$$  

• $$\frac{4}{7}\div\frac{1}{7}$$  

• $$\frac{4}{7}\times\frac{1}{7}$$  

• $$\frac{4}{7}\times\frac{7}{1}$$  

• $$\frac{7}{4}\times\frac{7}{1}$$  

Multiple Choice

You Do: Divide the following rational expression:
$$\frac{6xy^3}{8ab^2}\div\frac{3x^2y}{4ab^2}=$$  

• $$y^2$$  

• $$\frac{1}{x}$$  

• $$\frac{x^2}{2y}$$  

• $$\frac{y^2}{x}$$  

Multiple Choice

You Do:

• A

• B

• C

• D