The set {x in R: frac{14x}{x+1} - frac{9x-30} | vedclass

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(D) Given inequality: $\frac{14x}{x+1} - \frac{9x-30}{x-4} < 0$Simplify the expression by taking a common denominator:$\frac{14x(x-4) - (9x-30)(x+1)}{

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

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(D) Given inequality: $\frac{14x}{x+1} - \frac{9x-30}{x-4} Simplify the expression by taking a common denominator:$\frac{14x(x-4) - (9x-30)(x+1)}{(x+1)(x-4)} $\frac{14x^2 - 56x - (9x^2 + 9x - 30x - 30)}{(x+1)(x-4)} $\frac{14x^2 - 56x - (9x^2 - 21x - 30)}{(x+1)(x-4)} $\frac{14x^2 - 56x - 9x^2 + 21x + 30}{(x+1)(x-4)} $\frac{5x^2 - 35x + 30}{(x+1)(x-4)} Divide by $5$:$\frac{x^2 - 7x + 6}{(x+1)(x-4)} Factor the numerator:$\frac{(x-1)(x-6)}{(x+1)(x-4)} Using the wavy curve method (sign scheme) with critical points $-1, 1, 4, 6$:The expression is negative in the intervals $(-1, 1)$ and $(4, 6)$.Therefore,$x \in (-1, 1) \cup (4, 6)$.

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

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