What is ((x+3)/(x+16))> 3/(x-4) ?

The solution to ((x+3)/(x+16))> 3/(x-4) is x 10

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((x+3)/(x+16))> 3/(x-4)

(\frac{x + 3}{x + 16}) > \frac{3}{x - 4}

x < - 16 or - 6 < x < 4 or x > 10

Interval Notation

(- \infty, - 16) \cup (- 6, 4) \cup (10, \infty)

Solution steps

\frac{x + 3}{x + 16} > \frac{3}{x - 4}

Rewrite in standard form

\frac{x ^{2} - 4 x - 60}{( x - 4 ) ( x + 16 )} > 0

Factor

\frac{x ^{2} - 4 x - 60}{( x - 4 ) ( x + 16 )} : \frac{( x + 6 ) ( x - 10 )}{( x - 4 ) ( x + 16 )}

\frac{( x + 6 ) ( x - 10 )}{( x - 4 ) ( x + 16 )} > 0

Identify the intervals

x < - 16 or - 6 < x < 4 or x > 10

0 - 2

81 x^{2} + 4 = 0

\frac{x}{2} - 4 = 1

\frac{27 - 5}{15 - 3}

6 (3 x - 5) - 7 x = 25

What is ((x+3)/(x+16))> 3/(x-4) ?
The solution to ((x+3)/(x+16))> 3/(x-4) is x<-16\lor-6<x<4\lor x>10