Question

The fastest and right answer will be marked Brainliest​

Answer 1

${ \bold{ \boxed{ \boxed{ \red{ \huge\mathfrak{ \star \: answer \: \star}}}}}}$

${ \bold{ \underline{ Given \: \: function} : - }} \\ \\ { \bold{ \orange{ \mathtt{ \frac{ {x}^{2} + 6x - 7 }{ {x}^{2} + 1} \leqslant 2}}}}$

${ \bold{ \underline{To \: \: \: find} : - }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \bold{ \orange{ \mathtt{range \: \: of \: \: x}}}} \\ \\ { \bold{ \boxed{ \boxed{ \huge\mathfrak{ \green{ \star \: solution \: \star}}}}}}$

${ \bold { \orange{ \mathtt{ : \implies \: \frac{ {x}^{2} + 6x - 7 }{ {x}^{2} + 1 } \leqslant 2}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies {x}^{2} + 6x - 7 \leqslant 2 {x}^{2} + 2}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies - {x}^{2} + 6x - 9 \leqslant 0 }}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies {x}^{2} - 6x + 9 \geqslant 0}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies {x}^{2} - 3x - 3x + 9 \geqslant 0}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies \: x(x - 3) - 3(x - 3) \geqslant 0}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies(x - 3)(x - 3) \geqslant 0}}}} \\ \\ \\ { \bold { \orange{ \mathtt{ : \implies {(x - 3)}^{2} \geqslant 0}}}} \\ \\ \\ { \bold { \red{ \mathtt{ : \implies{ \boxed{ \boxed{x∈R}}}}}}}$

Answer 2

The answer above is right.