# Math Help - Differentiate Question

1. ## Differentiate Question

Question:
Differentiate with respect to x:

$y = \frac{x + 3}{x - 2}$

Any help is thanked.

2. I assume you learnt some differentiation.

Use the quotient rule:

when y = u/v

dy/dx = [v(du/dx) - u (dv/dx)] / v²

In your case y= (x+3)/(x-2) so

dy/dx = [(x-2)1 - (x+3)1] / (x-2)²

= (x-2-x-3)/ (x-2)²
= -5 / (x-2)²

I like to keep it in brackets, but you can expand if needed.

3. Originally Posted by name101
Question:
Differentiate with respect to x:

$y = \frac{x + 3}{x - 2}$

Any help is thanked.

\begin{aligned}
y &= \frac{{x + 3}}
{{x - 2}}\\
&= \frac{{x - 2 + 5}}
{{x - 2}}\\
&= 1 + 5\left( {x - 2} \right)^{ - 1}\\
y' &= - \frac{5}
{{\left( {x - 2} \right)^2 }}
\end{aligned}