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Rani Abbakkadevi

If 3x-1-2x-3=...

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If $3 (x - 1) - 2 (x - 3) = 6$ , then find the value of $\frac{{(x + 1)}^{2}}{x - 2} + \frac{4}{x + 1}$ , if $x$ ≠ -1, 2

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3 (x - 1) = 6 + 2 (x - 3)

,

find the value of

\frac{(x + 1)^{2}}{(x - 2)} + \frac{4}{(x + 1)}

{log}_{(2 x + 3)} (6 x^{2} + 23 x + 21) = 4 - {log}_{(3 x + 7)} (4 x^{2} + 12 x + 9)

, then find the value of

4 x + 1

f (x) = ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 4 x + 6 & 2 x^{2} + 4 x + 10 & 3 x^{2} - 2 x + 16 x - 2 & 2 x + 2 & 3 x - 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣

Q. The number of real values of

x

∣ ∣ ∣ ∣ \begin{matrix} x & 3 x + 2 & 2 x - 1 2 x - 1 & 4 x & 3 x + 1 7 x - 2 & 17 x + 6 & 12 x - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0

f (x) = ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 4 x + 6 & 2 x^{2} + 4 x + 10 & 3 x^{2} - 2 x + 16 x - 2 & 2 x + 2 & 3 x - 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣

. Then the value of

\int_{- 3}^{3} \frac{x^{2} s i n x}{1 + x^{6}} . f (x) d x

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