To factorise is to express a term as the product of its factors.

The quadratic formula is a formula for finding the solutions to any quadratic equation of the form $$ax^2 + bx + c = 0$$

Solving equations with algebraic fractions

Maths

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

Algebraic fractions

Convert to fractions over a common denominator.

What would be the most efficient first step to solve $${x+2\over 4x}+{3\over 6x}=4$$?

Which of these show all the solutions to the equation $${x+2\over 4x}+{3\over 6x}=4$$?

Which of these is a correct step when solving $${4\over x-2}-{6\over x-4}=-2$$?

Find all the solutions to $${4\over x-2}-{6\over x-4}=-2$$.

$${x^2 +2x-3\over (2x-3)(x-1)}={10x-15\over (2x-3)(x-1)}$$

$${(x+3)(x-1)\over 2(x-3)(x-1)}={10(x-3)\over 2(x-3)(x-1)}$$

Which of these is a correct step when solving  $${x+3\over 2x-3}={5\over x-1}$$?

Find all the solutions to $${x+3\over 2x-3}={5\over x-1}$$.

The solution to the equation $${2x\over 5}=4$$ is when $$x=$${{}}.

Find all the solutions to the equation $$x^2 + 5x +6 = 2$$.

Which of these is equivalent to $${x+3\over 2}\times {4\over x+4}$$?

Simplify $${x+1\over 3x}+{x+2\over 6x}$$.

This lesson will be removed by end of Summer Term 2025.

Solving equations with algebraic fractions

Lesson outcome

This lesson will be removed by end of Summer Term 2025.