Review question

# Which values can $x(x-3)/(x-4)$ take? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9391

## Question

If $y=\frac{x(x-3)}{x-4}$ and $x$ is real show that $y$ cannot take any value between $+1$ and $+9$.

Sketch the curve $y=\dfrac{x(x-3)}{x-4}$.

Using the same axes, sketch the curve $y=5/x$ and find its intersection with the line $x=4$.

Hence prove that the equation $\frac{5}{x}=\frac{x(x-3)}{x-4}$ has no positive root.