Rational Expressions Quiz: Simplify, Solve, and Exclusions

Question 1

Simplify and state any excluded values: $$\frac{x^2-9}{x-3}$$

Accepted Answer

$x+3$, with $x
eq 3$

Answer

$x+3$, with no excluded values

Answer

$\frac{x^2-9}{x-3}$, already simplest

Answer

$x-3$, with $x
eq 3$

Question 2

Divide and simplify: $$\frac{2x}{x-3}\div\frac{4}{x+1}$$

Accepted Answer

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

Answer

$\frac{8x}{(x-3)(x+1)}$

Answer

$\frac{2x}{x-3}\cdot\frac{4}{x+1}=\frac{8x}{(x-3)(x+1)}$

Answer

$\frac{2x(x+1)}{4(x-3)}$ (cannot reduce)

Question 3

Solve and state restrictions: $$\frac{x+2}{x-1}=\frac{x-1}{x+2}$$

Accepted Answer

$x=-	frac{1}{2}$, with $x
eq 1,-2$

Answer

$x=1$

Answer

$x=0$, with $x
eq 1,-2$

Answer

$x=-2$

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