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If $x$ is real, the value of $\large\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval
\[\begin {array} {1 1} (a)\;\bigg[\frac{1}{3},3\bigg] & \quad (b)\;\bigg[\frac{1}{5},5 \bigg] \\ (c)\;\bigg[\frac{1}{6},6\bigg] & \quad (d)\;\bigg[\frac{1}{7},7\bigg] \end {array}\]
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