On the same axes, sketch the graphs of $y=x+2+\frac{1}{x-1}$ and $y=\left| 2x+2 \right|$, statin

Question

On the same axes, sketch the graphs of $y=x+2+\frac{1}{x-1}$ and $y=\left| 2x+2 \right|$, stating the coordinates of any points of intersection with the axes, turning points and the equations of any asymptotes.[5] Hence solve the inequality $x+2+\frac{1}{x-1}>\left| 2x+2 \right|$, giving your answers in exact form.[5]

Accepted Answer

(ii) $\frac{-1-\sqrt{37}}{6} < x < \frac{1-\sqrt{5}}{2}$ or $1 < x < \frac{1+\sqrt{5}}{2}$

2021 RI Promo Q6

2021 RI Promo Q6

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