What is (x^2-3x+2)/(x^2+2x+6)<3 ?

The solution to (x^2-3x+2)/(x^2+2x+6)<3 is True for all x

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(x^2-3x+2)/(x^2+2x+6)<3

\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 6} < 3

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 6} < 3

Rewrite in standard form

\frac{- 2 x ^{2} - 9 x - 16}{x ^{2} + 2 x + 6} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 2 x ^{2} + 9 x + 16 ) ) ( - 1 )}{x ^{2} + 2 x + 6} > 0 \cdot (- 1)

Simplify

\frac{2 x ^{2} + 9 x + 16}{x ^{2} + 2 x + 6} > 0

Identify the intervals

True for all x

4 x^{2} - 64 y^{2}

x^{2} - 20 x + 85 = - 6

3 m^{3} - m^{2} + 9 m - 3

30 \cdot \frac{1}{3}

\frac{x ^{3} - 6 x ^{2}}{x - 2} > 0

What is (x^2-3x+2)/(x^2+2x+6)<3 ?
The solution to (x^2-3x+2)/(x^2+2x+6)<3 is True for all x