What is (x+1)/(x-2)< 6/(x-3) ?

The solution to (x+1)/(x-2)< 6/(x-3) is 4-sqrt(7)<x<2\lor 3<x<4+sqrt(7)

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(x+1)/(x-2)< 6/(x-3)

\frac{x + 1}{x - 2} < \frac{6}{x - 3}

4 - 7 < x < 2 or 3 < x < 4 + 7

Interval Notation

(4 - 7, 2) \cup (3, 4 + 7)

Decimal Notation

1.35424 \dots < x < 2 or 3 < x < 6.64575 \dots

Solution steps

\frac{x + 1}{x - 2} < \frac{6}{x - 3}

Rewrite in standard form

\frac{x ^{2} - 8 x + 9}{( x - 2 ) ( x - 3 )} < 0

Factor

x^{2} - 8 x + 9 : (x - 4 - 7) (x - 4 + 7)

\frac{( x - 4 - 7 ) ( x - 4 + 7 )}{( x - 2 ) ( x - 3 )} < 0

Identify the intervals

4 - 7 < x < 2 or 3 < x < 4 + 7

343 a^{3} + 216

∣ 2 x - 3 ∣ > 4

x^{2} - x - 12 \leq 0

2 x^{2} - 4 x - 2

- 6 < 3 k - 9 \leq 0

What is (x+1)/(x-2)< 6/(x-3) ?
The solution to (x+1)/(x-2)< 6/(x-3) is 4-sqrt(7)<x<2\lor 3<x<4+sqrt(7)