Recently published items

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Rearrange a specific formula. No randomisation.