left{x in R: frac{14 x}{x+1}-frac{9 x-30}{x-4 | vedclass

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(D) Given inequality: $\frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0$Simplify the expression:$\frac{14 x(x-4)-(9 x-30)(x+1)}{(x+1)(x-4)} < 0$$\frac{14 x^2-5

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$(-1,1) \cup(4,6)$

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(D) Given inequality: $\frac{14 x}{x+1}-\frac{9 x-30}{x-4} Simplify the expression:$\frac{14 x(x-4)-(9 x-30)(x+1)}{(x+1)(x-4)} $\frac{14 x^2-56 x-(9 x^2+9 x-30 x-30)}{(x+1)(x-4)} $\frac{14 x^2-56 x-(9 x^2-21 x-30)}{(x+1)(x-4)} $\frac{5 x^2-35 x+30}{(x+1)(x-4)} $\frac{5(x^2-7 x+6)}{(x+1)(x-4)} $\frac{5(x-1)(x-6)}{(x+1)(x-4)} Using the wavy curve method (sign scheme) on the number line with critical points $-1, 1, 4, 6$:The expression is negative in the intervals $(-1, 1)$ and $(4, 6)$.Thus,$x \in (-1, 1) \cup (4, 6)$.

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

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