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Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

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