Moderate -0.3 This is a straightforward application of the quotient rule to find dy/dx, followed by evaluating at x=1 to get the gradient, then using point-slope form to write the tangent equation. All steps are routine and mechanical with no conceptual challenges, making it slightly easier than average but not trivial due to the algebraic manipulation required.
2 A curve has equation \(y = \frac { 2 + 3 \ln x } { 1 + 2 x }\).
Find the equation of the tangent to the curve at the point \(\left( 1 , \frac { 2 } { 3 } \right)\). Give your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
2 A curve has equation $y = \frac { 2 + 3 \ln x } { 1 + 2 x }$.\\
Find the equation of the tangent to the curve at the point $\left( 1 , \frac { 2 } { 3 } \right)$. Give your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.\\
\hfill \mbox{\textit{CAIE P2 2023 Q2 [5]}}