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

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

Add/subtract fractions and reduce to lowest form.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Questions testing understanding of numerators and denominators of numerical fractions.

Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.

Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.

Questions testing addition, subtraction, multiplication of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.

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

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.

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

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

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