Unit 6 Review (Algebra 2)

​Unit 6 (Rationals) Review

​Algebra 2

​Sections in Unit 6

• 6.1 Simplifying Rational Expressions

• 6.2 Multiplying/Dividing Rational Expressions

• 6.3 Adding Rational Expressions

• 6.4 Subtracting Rational Expressions

• 6.5 Solving Rational Equations

• 6.6 Graphing Simple Rational Functions

Multiple Choice

Find the LCD of $$\frac{x+7}{x^2+5x+6}$$ and $$\frac{x-7}{\left(x+3\right)^2}$$ .

• $$\left(x+7\right)\left(x-7\right)$$

• $$\left(x+2\right)\left(x+3\right)$$

• $$\left(x+2\right)\left(x+3\right)^2$$

• $$\left(x+7\right)\left(x-7\right)\left(x+2\right)\left(x+3\right)$$

Multiple Select

Which values of x are excluded from the domain of $$\frac{2x-2}{x-7}-\frac{3}{x\left(x+2\right)}$$ ? Select ALL that apply.

• 2

• 7

• 3

• 0

• -2

Multiple Choice

Simplify $$\frac{2x^3-x^2-3x}{2x^2-3x}$$ .

• $$-x^2$$

• $$x+1$$

• $$2x-3$$

• $$\frac{x+1}{2x-3}$$

Multiple Choice

Simplify $$\frac{2x+14}{x^2+15x+56}\cdot\frac{x^2+3x-40}{6x}$$ .

• $$\frac{x-5}{3x}$$

• $$\frac{3x}{x-5}$$

• $$\frac{x+7}{3x}$$

• $$\frac{2}{x+7}$$

Multiple Choice

Simplify $$\frac{x^2-49}{x^4+7x^3}\div\frac{x^2-x-42}{3x}$$ .

• $$\frac{3x}{\left(x+6\right)}$$

• $$\frac{x}{x+6}$$

• $$\frac{x+6}{3}$$

• $$\frac{3}{x^2\left(x+6\right)}$$

Multiple Choice

Simplify $$\frac{5x}{y^2}+\frac{1}{4x}$$ .

• $$\frac{x}{4y^2}$$

• $$\frac{5x+1}{4xy^2}$$

• $$\frac{5}{4xy^2}$$

• $$\frac{20x^2+y^2}{4xy^2}$$

Multiple Choice

Simplify $$\frac{1}{x+4}+\frac{7}{x}$$ .

• $$\frac{7x+4}{x+4}$$

• $$\frac{8x+28}{x\left(x+4\right)}$$

• $$\frac{x\left(x+4\right)}{8}$$

• $$\frac{8}{x\left(x+4\right)}$$

Multiple Choice

Simplify. $$\frac{3}{x-3}-\frac{3x}{x-5}$$ .

• $$\frac{3}{x+5}$$

• $$\frac{-3x^2+12x-15}{\left(x-5\right)\left(x-3\right)}$$

• $$\frac{x^2+17}{\left(x-3\right)\left(x-5\right)}$$

• $$\frac{3-3x}{\left(x-3\right)\left(x-5\right)}$$

Multiple Choice

Simplify $$\frac{x-\frac{4}{x}}{\frac{x+5}{6}+\frac{1}{x}}$$ .

• $$\frac{4\left(x+2\right)}{x\left(x+3\right)}$$

• $$\frac{4}{\left(x+3\right)}$$

• $$\frac{6\left(x-2\right)}{x+3}$$

• $$\frac{\left(x+2\right)\left(x+3\right)}{x}$$

Fill in the Blank

One solution of $$\frac{x+8}{x+6}=\frac{-5}{x}$$ is $$x=-3$$ . What is the other?

Type your numerical answer into the box.

x = _____?

Fill in the Blank

In the following equation, one solution, $$x=1$$ , is thrown out because of division by 0. Solve and find the solution that is kept.

$$1+\frac{5}{x-1}=\frac{3x+7}{x^2-1}$$

x = ______ and 1 (excluded)

Multiple Choice

Which rational function would have a Vertical Asymptote of $$x=2$$ , a Horiztonal Asymptote of $$y=-3$$ , be stretched by factor of 4, and reflected vertically over the x-axis?

• $$y=-\frac{2}{x-4}+3$$

• $$y=\frac{4}{x+2}-3$$

• $$y=\frac{3}{x-4}-2$$

• $$y=-\frac{4}{x-2}-3$$

Multiple Choice

Which equation matches the function shown in the graph?

• $$y=\frac{2}{x-4}+1$$

• $$y=\frac{3}{x+1}+4$$

• $$y=-\frac{1}{x+1}+4$$

• $$y=\frac{3}{x-1}+4$$

​That's it!

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