Edexcel A-Level Mathematics A2 P3.1.1 Simplification of Rational Denominators of Rational Questions

Practise rewriting rational expressions by factorising, using algebraic division and comparing coefficients to find constants in required forms.

Exam points

use polynomial division or coefficient comparison to rewrite a rational expression
factorise denominators and cancel common factors to show a simplified function form

[Maximum number: 3]

The function f is defined by

f(x)=\frac{5x}{x^2+7x+12}+\frac{5x}{x+4},\qquad x>0

Show that $f(x)=\frac{5x}{x+3}$ .

\begin{aligned}\frac{5x}{x^2+7x+12}+\frac{5x}{x+4}&=\frac{5x+5x(x+3)}{(x+3)(x+4)}\\&=\frac{5x^2+20x}{(x+3)(x+4)}\\&=\frac{5x(x+4)}{(x+3)(x+4)}=\frac{5x}{x+3}.\end{aligned}

M1: common denominator.
A1: correct unsimplified fraction.
A1*: reaches the given result.

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