Multiply $36$ by $ \dfrac{y}{10x-9y} $ to get $ \dfrac{ 36y }{ 10x-9y } $.

Step 1: Write $ 36 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 36 \cdot \frac{y}{10x-9y} & \xlongequal{\text{Step 1}} \frac{36}{\color{red}{1}} \cdot \frac{y}{10x-9y} \xlongequal{\text{Step 2}} \frac{ 36 \cdot y }{ 1 \cdot \left( 10x-9y \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36y }{ 10x-9y } \end{aligned} $$

Add $ \dfrac{36y}{10x-9y} $ and $ \dfrac{40}{9y-10x} $ to get $ \dfrac{ \color{purple}{ -360xy+324y^2+400x-360y } }{ -100x^2+180xy-81y^2 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ -10x+9y }$ and the second by $\color{blue}{ 10x-9y }$.

$$ \begin{aligned} \frac{36y}{10x-9y} + \frac{40}{9y-10x} & = \frac{ 36y \cdot \color{blue}{ \left( -10x+9y \right) }}{ \left( 10x-9y \right) \cdot \color{blue}{ \left( -10x+9y \right) }} + \frac{ 40 \cdot \color{blue}{ \left( 10x-9y \right) }}{ \left( 9y-10x \right) \cdot \color{blue}{ \left( 10x-9y \right) }} = \\[1ex] &=\frac{ \color{purple}{ -360xy+324y^2 } }{ -100x^2+90xy+90xy-81y^2 } + \frac{ \color{purple}{ 400x-360y } }{ -100x^2+90xy+90xy-81y^2 } = \\[1ex] &=\frac{ \color{purple}{ -360xy+324y^2+400x-360y } }{ -100x^2+180xy-81y^2 } \end{aligned} $$