Simple question about pseudorandom generator
I assume you mean a cryptographic PRG.

Let's assume on the contrary that the $G&#39;$ is not secure. So let $A$ be a probabilistic Turing machine that distinguishes the output of $G&#39;$ from uniformly random bits.

Let $x_1,x_2$ be $k$ bit random strings, and let $z_1,z_2$ be $k+1$ bit random strings.

We have that $A$ distinguishes the distribution of strings $D_0 : G(x_1)G(x_2)$ and 
$D_2: z_1z_2$.

Consider now the hybrid distribution of strings given by $D_1: G(x_1)z_2$.

By the triangle inequality $A$ also distinguishes between either $D_0$ and $D_1$ or between $D_1$ and $D_2$.

Assume without loss of generality that  $A$ distinguishes between $D_0$ and $D_1$.
Then we can break $G$ as follows. On input $y$, pick uniformly random $k$ bit string $x_1$ and give the string $G(x_1)y$ to $A$.