What is 4/(x-3)<x+1 ?

The solution to 4/(x-3) 1+2sqrt(2)

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4/(x-3)<x+1

\frac{4}{x - 3} < x + 1

1 - 22 < x < 3 or x > 1 + 22

Interval Notation

(1 - 22, 3) \cup (1 + 22, \infty)

Decimal Notation

- 1.82842 \dots < x < 3 or x > 3.82842 \dots

Solution steps

\frac{4}{x - 3} < x + 1

Rewrite in standard form

\frac{- x ^{2} + 2 x + 7}{x - 3} < 0

Factor

- x^{2} + 2 x + 7 : - (x - 1 - 22) (x - 1 + 22)

\frac{- ( x - 1 - 2 2 ) ( x - 1 + 2 2 )}{x - 3} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 - 2 2 ) ( x - 1 + 2 2 ) ) ( - 1 )}{x - 3} > 0 \cdot (- 1)

Simplify

\frac{( x - 1 - 2 2 ) ( x - 1 + 2 2 )}{x - 3} > 0

Identify the intervals

1 - 22 < x < 3 or x > 1 + 22

11 \cdot \frac{1}{2}

- 2 (x - 1)^{2} = 36

\frac{2 ( 9 ) ^{\frac{3}{2}}}{3}

\frac{( 12 x ^{2} y ^{6} ) ^{2}}{8 x ^{4} y ^{7}}

3 x \cdot 5 x = 5

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