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Rational Expression

Solve for x...

Question

Solve for $x$ in the equation $\frac{[x^{2} - (x + 1) (x + 2)]}{5 x + 1} = 6$ . Find the value of $66 x + 32$

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Solution

$(\frac{x^{2} - (x^{2} + 3 x + 2)}{5 x + 1}) = 6 x^{2} - x^{2} - 3 x - 2 = 30 x + 6 - 2 - 6 = 30 x + 3 x ∴ 33 x = - 8 ∴ x = (\frac{- 8}{33}) w e h a v e t o f i n d 66 x + 32 = 66 \times (\frac{- 8}{33}) + 32 = - 16 + 32 = 16$

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\frac{x^{2} - (x + 1) (x + 2)}{5 x + 1} = 6

Q. Largest interval in which the inequality

∣ ∣ ∣ \frac{(x + 3) (2 + x)}{(x - 1) (x - 5)} ∣ ∣ ∣ > \frac{x^{2} + 5 x + 6}{x^{2} - 6 x + 5}

x : ∣ ∣ ∣ \frac{x^{2} + 6}{5 x} ∣ ∣ ∣ \geq 1

\frac{x^{2} - (x + 1) (x + 2)}{5 x + 1} = 6

x

(5 x + 1) (x + 3) - 8

=

5 (x + 1) (x + 2)

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