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Manipulate surds and rationalise the denominator of a fraction when it is a surd.

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

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Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Add/subtract fractions and reduce to lowest form.

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

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Add, subtract, multiply and divide algebraic fractions.

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Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Differentiate $\displaystyle ax^b, ax^b+cx^{1/d}, \frac{a}{x^{1/c}}+\frac{b}{x^{-1/d}}+c$ with respect to $x$.