Question

X²+6x-7/x²+1<2

X square plus 6 X minus 7 divided by X square plus 1 is smaller than or equal to 2.

Find the solutions of the inequality
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Answer 1

${x}^{2} + 6x - 7 < 2 {x}^{2} + 2 \\ - {x}^{2} + 6x - 9 < 0 \\ {x}^{2} - 6x + 9 > 0 \\ note \\ {x}^{2} - 6x + 9 = 0\\ {x}^{2} - 3x - 3x + 9 = 0 \\ (x - 3)(x - 3) = 0 \\ x = 3 \: and \: 3 \\ so \: (3 \: \: \infty )( 3 \: \: \: - \infty ) \\ (3 \: \: \: \: + - \infty )$