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Puzzles
Algebraic fractions
Permanent link to this puzzle:
mscroggs.co.uk/puzzles/91
Source:
UKMT Senior Maths Challenge 2014
Given that
$$\frac{3x+y}{x-3y}=-1$$
what is the value of
$$\frac{x+3y}{3x-y}$$
?
Show answer & extension
Hide answer & extension
$$\frac{3x+y}{x-3y}=-1$$
implies that
$$3x+y=3y-x\\ 2x=y$$
This means that
$$\frac{x+3y}{3x-y}=\frac{x+6x}{3x-2x}\\ =\frac{7x}{x}\\=7$$
Extension
Given that
$$\frac{3x+y}{x-3y}=-k$$
what is the value of
$$\frac{x+3y}{3x-y}$$
?
For which values of \(k\) is the answer an integer?
Tags:
algebra
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