Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

First part: Express  $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d},\;a=-c$. Numerator is an integer.

Second part: $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d}+ \frac{r}{sx+t}$ as single fraction 

First part: express as a single fraction: $\displaystyle \frac{a}{x + b} +  \frac{c}{x + d},\; a \neq -c$.

Second part: Find $\displaystyle \frac{a}{x + b} + \frac{c}{x + d}+\frac{r}{x+t}$ as a single fraction.

First part: express as a single fraction: $\displaystyle \frac{a}{px + b} +  \frac{c}{qx + d}$.

Second part: Find $\displaystyle \frac{a}{px + b} + \frac{c}{qx + d}+\frac{r}{sx+t}$ as a single fraction.

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} +\frac{c}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

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Practice with adding, subtracting and dividing basic algebraic fractions

A quadratic function is given. The graph of the function is drawn with three coordinates on the graph, without any x or y ticks.  The $x$ coordinate is given for a couple and $y$ coordinate given for the third, and coordinates are asked for.

Practice with adding, subtracting and dividing basic algebraic fractions

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

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Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Entering numbers and algebraic symbols  in Numbas.

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

Express $\displaystyle b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$