Dividing algebraic fractions question where the result does not require any cancellation

(ax+b)/(mx+n)+(cx+d)/(px+q)

Adding algebraic fractions with linear expressions in the numerators

simplifying pL1^a/n+kL2^bL1^c/m

Adding two algebraic fractions with the same variable in the numberators.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

Questions for practising algebraic methods for solving linear simultaneous equations

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Using indices rules to write powers as negative powers

Writing negative powers as fractions

Writing fractins as negative powers

Using indices rules to write expressions as negative powers.

Using indices rules to write fractions as negative powers.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Using rules for roots and powers to write expressions with only powers

Using indices to write roots as fractional powers

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Calculate an answer involving a fractional index.

Simplifying expressions from $(z^m)^n$ to $z^{mn}$. 

Simplifying expressions from $y^m\div y^n$ to $y^{m-n}$.