Solving equations with algebraic fractions | Maths | Quizalize & Oak National Academy

Starter quiz

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

'10' ✓
Solve ${12\over 5x} = 8$ .

$2\over 15$

$3\over 10$ ✓

$4\over 5$

$10\over 3$

$15\over 2$
Factorise $x^2 + 3x -4$ .

$(x-2)(x-2)$

$(x-1)(x+3)$

$(x-1)(x+4)$ ✓

$(x-4)(x+3)$
Find all the solutions to the equation $x^2 + 5x +6 = 2$ .

$x=-2$

$x=-2$ and $x=-3$

$x=-1$ and $x=-4$ ✓

$x=1$ and $x=4$

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

$2x+12\over 8$

$2x+6\over x+4$ ✓

$x+3\over 2x+2$

$4x+3\over 2x+4$

$x^2 + 7x +12\over 8$
Simplify ${x+1\over 3x}+{x+2\over 6x}$ .

$2x+3\over 6x$

$2x+3\over 9x$

$3x+3\over 18x$

$3x+4\over 6x$ ✓

$3x^2+1\over 6x^2$

Exit quiz

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

Convert to fractions over a common denominator. ✓

Factorise all expressions.

Multiply all terms by $6x$ .

Subtract 2 from both sides.

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

$x=-{8\over 3}$

$x=0$ or $x={4\over 7}$

$x={5\over 39}$

$x={4\over 15}$ ✓

$x={1\over 3}$
Which of these is a correct step when solving ${4\over x-2}-{6\over x-4}=-2$ ?

${4\over x-4}=-2$

${4\over x-2}-{4\over x-4} =0$

${-2x-28\over (x-4)(x-2)} =-2$

${-2x-6\over (x-4)(x-2)} =-2$

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

$x=-6$ or $x=1$

$x=-2$ or $x=5$

$x=2$ or $x=3$

$x=2$ or $x=5$

$x=6$ or $x=1$ ✓
Which of these is a correct step when solving ${x+3\over 2x-3}={5\over x-1}$ ?

$x^2-3=10x-15$

${-1(x-3)\over 2(x-3)}={5\over x-1}$

${x+3\over 2x-3}={5+x+2\over 2x-3}$

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

${(x+3)(x-1)\over 2(x-3)(x-1)}={10(x-3)\over 2(x-3)(x-1)}$
Find all the solutions to ${x+3\over 2x-3}={5\over x-1}$ .

$x=2$ or $x=6$ ✓

$x=2$ or $x=-6$

$x=-2$ or $x=6$

$x=-2$ or $x=-6$

Worksheet

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Lesson Details

Key learning points

Before performing any operation, equivalent fractions should be considered.
Algebraic fractions follow the same rules as fractions.
It is important to maintain equivalence between two algebraic statements.
Multiplying both connected statements by the reciprocal can simplify.

Common misconception

Assuming that 'cross multiplying' is always the best way to solve equations with fractions on both sides.

Examples are included in the lesson where this results in unnecessary quadratic equations. Factorising and looking for common factors allows pupils to spot efficient methods. This also links with fraction skills of finding a common denominator.

Keywords

Factorise - To factorise is to express a term as the product of its factors.
Quadratic formula - The quadratic formula is a formula for finding the solutions to any quadratic equation of the form $ax^2 + bx + c = 0$