Rational algebraic expressions Questionbank

$\frac{x + 2}{x(x + 2)}$

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

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

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

True, because the terms $a$ and $b$ are common to both the numerator and the denominator.

True, because $a^2 + b^2$ is equivalent to $(a + b)^2$.

False, because terms in a sum cannot be cancelled individually; only common factors can be simplified.

False, because the expression $\dfrac{a^2 + b^2}{a + b}$ is equivalent to $a - b$.

$x = \frac{yz}{z-y}$

$x = z - y$

$x = \frac{yz}{y-z}$

$x = \frac{y-z}{yz}$

$x = \frac{2y}{1 - y}$

$x = \frac{2y}{y - 1}$

$x = \frac{y - 2}{y}$

$x = \frac{1 - y}{2y}$

$x = \frac{y}{y - 1}$

$x = \frac{1 - y}{y}$

$x = \frac{y}{1 - y}$

$x = y - 1$

The result should be $\frac{1}{x - 2}$

The student correctly simplified the expression

The expression cannot be simplified

The student should have cancelled $x$ instead of $(x + 2)$

h = 3V - \pi r^2

h = \frac{3V}{\pi r^2}

h = \frac{\pi r^2}{3V}

h = \frac{V}{3\pi r^2}

$\frac{x}{x^2 - 4}$

$\frac{x^2 - 4}{x - 2}$

$\frac{x + 1}{x}$

$\frac{x}{x^2 + 4}$

True

False

$\frac{x-1}{1-x}$

$1$

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

$-1$