docs: grammar (#3059)

minor typos/grammar

Author: Soupedenuit

docs/api/README.md

@@ -165,11 +165,11 @@ If you add a `target="_blank"` to your `a` element, you must omit the `@click="n
 
 ## `<router-view>`
 
-The `<router-view>` component is a functional component that renders the matched component for the given path. Components rendered in `<router-view>` can also contain its own `<router-view>`, which will render components for nested paths.
+The `<router-view>` component is a functional component that renders the matched component for the given path. Components rendered in `<router-view>` can also contain their own `<router-view>`, which will render components for nested paths.
 
 Any non-name props will be passed along to the rendered component, however most of the time the per-route data is contained in the route's params.
 
-Since it's just a component, it works with `<transition>` and `<keep-alive>`. When using the both together, make sure to use `<keep-alive>` inside:
+Since it's just a component, it works with `<transition>` and `<keep-alive>`. When using them both together, make sure to use `<keep-alive>` inside:
 
 ```html
 <transition>