Resolve 8x-43x2-2x-1 into partial fractions-

The correct option is D 53x+1+ 1x 1 Let 8x 43x^2 2x 1=8x 4(x 1)(3x+1)=A(x 1)+B(3x+1) ..... (1)Multiply (x 1)(3x+1) on both the sides, we get ...

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Standard IX

Mathematics

Polynomial and Its General Form

Resolve 8x-...

Question

Resolve $\frac{8 x - 4}{3 x^{2} - 2 x - 1}$ into partial fractions.

\frac{5}{x + 1} + \frac{1}{x + 1}

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\frac{4 x}{3 x + 1} + \frac{x}{x - 1}

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\frac{1}{3 x + 1} - \frac{1}{x + 1}

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\frac{5}{3 x + 1} + \frac{1}{x - 1}

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Solution

The correct option is D $\frac{5}{3 x + 1} + \frac{1}{x - 1}$
Let $\frac{8 x - 4}{3 x^{2} - 2 x - 1} = \frac{8 x - 4}{(x - 1) (3 x + 1)} = \frac{A}{(x - 1)} + \frac{B}{(3 x + 1)}$ ..... (1)
Multiply $(x - 1) (3 x + 1)$ on both the sides, we get
$8 x - 4 = A (3 x + 1) + B (x - 1)$
Put $x = 1$ to find value of A
$∴ 8 (1) - 4 = A [3 (1) + 1] \Rightarrow A = 1$
Put $x = - \frac{1}{3}$ to find value of B
$∴ 8 (\frac{- 1}{3}) - 4 = B (\frac{- 1}{3} - 1) \Rightarrow B = 5$
Substitute the values of A and B in equation (1), we get
$\frac{8 x - 4}{3 x^{2} - 2 x - 1} = \frac{1}{(x - 1)} + \frac{5}{(3 x + 1)}$

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Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

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Resolve 8x−43x2−2x−1 into partial fractions.

Resolve $\frac{8 x - 4}{3 x^{2} - 2 x - 1}$ into partial fractions.