L2 Algebra
Question Bank
Simplify fully:
$\frac{x^2 - 9}{x^2 + 5x + 6}$
Simplify fully:
$\frac{2x^2 + 7x - 15}{4x^2 - 9}$
Express $\displaystyle \frac{x+1}{3} + \frac{x-2}{4}$ as a single fraction.
Simplify fully: $\displaystyle \frac{2x^2 - x - 15}{4x^2 - 25}$.
Simplify fully: $\displaystyle \frac{3x^2-6x-9}{x^2+2x-15}$
Write as a single fraction: $\displaystyle \frac{3}{x-2} - \frac{4x}{x+1}$
Solve the equation $\displaystyle \frac{x^2+2x-8}{x^2-x-2} = 3$
Express $\displaystyle \frac{2x+1}{4} - \frac{x-3}{3}$ as a single fraction.
Write the following as a single fraction in its simplest form: $\displaystyle \frac{3}{2x} - \frac{x+1}{x^2} + \frac{2}{5}$
Write as a single fraction in its simplest form:
$\frac{3}{x - 2} - \frac{2}{x^2 - 4}$
Solve the equation
$\frac{2}{x} + \frac{3}{x + 1} = 2$
Prove that for any distinct real numbers $a$ and $b$, the following identity is true:
$\small \left(\frac{a}{b} - \frac{b}{a}\right) \div \left(\frac{1}{b} - \frac{1}{a}\right) = a+b$
A cyclist rides a 30 km section of the Otago Central Rail Trail.
On a calm day, the cyclist's average speed is $v$ km/h. On a windy day, the average speed is 5 km/h slower, and the ride takes 30 minutes longer.
Form an equation and solve it to find the cyclist's average speed on a calm day.
Show that the expression $\displaystyle \frac{x^3 - x^{-1}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}}$ can be simplified to $\displaystyle \frac{(x-1)(x^2+1)}{x^{\frac{5}{2}}}$.