How many real roots does $(x-1)(x+2)(x+3)=3x$ have?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Express \(\dfrac{3x}{(x-1)(x+2)}\) in partial fractions.

Show that \(\dfrac{dy}{dx}\) is negative at all points on the graph of \[y=\frac{3x}{(x-1)(x+2)}.\]

Sketch this graph, showing the two asymptotes parallel to the \(y\)-axis and the asymptote perpendicular to the \(y\)-axis.

By sketching on the same diagram a second graph (the equation of which should be stated), or otherwise, find the number of real roots of the equation \[(x-1)(x+2)(x+3)=3x.\]