As x -intercept is a point on the graph where \(\displaystyle{y}={0}\),

\(\displaystyle{\frac{{{6}}}{{{x}^{{{2}}}+{4}{x}-{7}}}}={0}\) implies there is no solution for \(\displaystyle{x}\in{R}\).

\(\displaystyle\therefore\) There is no x -intercept point.

As y -intercept is a point on the graph where \(\displaystyle{x}={0}\),

\(\displaystyle{y}={\frac{{{6}}}{{{0}^{{{2}}}+{4}{\left({0}\right)}-{7}}}}\)

\(\displaystyle{y}=-{\frac{{{6}}}{{{7}}}}\) \(\displaystyle\therefore\) y-intercept is \(\displaystyle{\left({0},-{\frac{{{6}}}{{{7}}}}\right)}\)

\(\displaystyle{\frac{{{6}}}{{{x}^{{{2}}}+{4}{x}-{7}}}}={0}\) implies there is no solution for \(\displaystyle{x}\in{R}\).

\(\displaystyle\therefore\) There is no x -intercept point.

As y -intercept is a point on the graph where \(\displaystyle{x}={0}\),

\(\displaystyle{y}={\frac{{{6}}}{{{0}^{{{2}}}+{4}{\left({0}\right)}-{7}}}}\)

\(\displaystyle{y}=-{\frac{{{6}}}{{{7}}}}\) \(\displaystyle\therefore\) y-intercept is \(\displaystyle{\left({0},-{\frac{{{6}}}{{{7}}}}\right)}\)