The problem has three parts: (a) Factorize completely $2\pi h + 2\pi r^2$. (b) Express $\frac{4}{x+5} - \frac{3}{x}$ as a single fraction in its simplest form. (c) Solve the simultaneous equations: $2x+3y=13$ and $x+2y=8$.

1. Problem Description

The problem has three parts:

(a) Factorize completely $2\pi h + 2\pi r^2$.

(b) Express $\frac{4}{x+5} - \frac{3}{x}$ as a single fraction in its simplest form.

(c) Solve the simultaneous equations: $2x+3y=13$ and $x+2y=8$.

2. Solution Steps

(a) Factorizing $2\pi h + 2\pi r^2$:

We can factor out the common factor $2\pi$ from both terms.

$2\pi h + 2\pi r^2 = 2\pi(h + r^2)$.

Alternatively, if $r$ represents radius, it should be $2\pi rh + 2\pi r^2$. In that case, we factor out $2\pi r$:

$2\pi rh + 2\pi r^2 = 2\pi r(h + r)$.

Given the prompt, it looks like the intended question was $2\pi rh + 2\pi r^2$.

(b) Expressing $\frac{4}{x+5} - \frac{3}{x}$ as a single fraction:

To subtract the two fractions, we need a common denominator, which is $x(x+5)$.

$\frac{4}{x+5} - \frac{3}{x} = \frac{4x}{x(x+5)} - \frac{3(x+5)}{x(x+5)}$

$= \frac{4x - 3(x+5)}{x(x+5)}$

$= \frac{4x - 3x - 15}{x(x+5)}$

$= \frac{x - 15}{x(x+5)}$

$= \frac{x-15}{x^2 + 5x}$

(c) Solving the simultaneous equations:

$2x + 3y = 13$ (1)

$x + 2y = 8$ (2)

From equation (2), we can express $x$ in terms of $y$: $x = 8 - 2y$.

Substitute this into equation (1):

$2(8-2y) + 3y = 13$

$16 - 4y + 3y = 13$

$16 - y = 13$

$y = 16 - 13$

$y = 3$

Now, substitute $y=3$ into the equation $x = 8 - 2y$:

$x = 8 - 2(3)$

$x = 8 - 6$

$x = 2$

So, the solution is $x=2$ and $y=3$.

3. Final Answer

(a) $2\pi r(h+r)$

(b) $\frac{x-15}{x(x+5)}$

x = 2

y = 3