For all x- 3- simplify 3x2-11x-69-x2-

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Standard XII

Mathematics

Integration by Partial Fractions

For all x± ...

Question

For all $x \neq \pm 3$ , simplify $\frac{3 x^{2} - 11 x + 6}{9 - x^{2}}$ .

\frac{2 - 3 x}{x - 3}

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\frac{2 - 3 x}{x + 3}

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\frac{2 x - 3}{x - 3}

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\frac{3 x - 2}{x + 3}

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\frac{3 x - 2}{x - 3}

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Solution

The correct option is B $\frac{2 - 3 x}{x + 3}$
In above numerator can be written as $3 x^{2} - 11 x + 6 = (3 - x) (2 - 3 x)$
And denominator can be written as $9 - x^{2} = (3 - x) (3 + x)$
So, $\frac{n u m e r a t o r}{d e n o m i n a t o r} = \frac{[(3 - x) (2 - 3 x)]}{[(3 - x) (3 + x)]} = \frac{(2 - 3 x)}{(3 + x)}$

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Similar questions

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

Solve :

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

Q. Divide

2 x^{3} + 3 x^{2} - 11 x - 6

x^{2} + x - 6

Q. Simplify:

\frac{3 x^{2} - 3}{x^{2} - 2 x - 3}

Q. Solve the equations:

\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}

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For all x≠±3, simplify 3x2−11x+69−x2.

The correct option is B 2−3xx+3In above numerator can be written as 3x2−11x+6=(3−x)(2−3x)And denominator can be written as 9−x2=(3−x)(3+x)So, numeratordenominator=[(3−x)(2−3x)][(3−x)(3+x)]=(2−3x)(3+x)

For all $x \neq \pm 3$ , simplify $\frac{3 x^{2} - 11 x + 6}{9 - x^{2}}$ .