The sum of the reciprocals of x-3x2-1 and x2-9x2-3 is

The correct option is B x^3 2x^2+xx^2 9 Consider #10;the sum of the reciprocals of , #10; #10; x+3x^2+1 #10;and x^2 9x^2+3 #10; #10 ...

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Standard X

Mathematics

Applications of Second Degree Equations

The sum of th...

Question

The sum of the reciprocals of $\frac{x + 3}{x^{2} + 1}$ and $\frac{x^{2} - 9}{x^{2} + 3}$ is

\frac{x^{3} + 2 x^{2} - x}{x^{2} - 9}

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\frac{x^{3} - 2 x^{2} + x}{x^{2} - 9}

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Solution

The correct option is B $\frac{x^{3} - 2 x^{2} + x}{x^{2} - 9}$
Consider the sum of the reciprocals of ,

$\frac{x + 3}{x^{2} + 1}$ and $\frac{x^{2} - 9}{x^{2} + 3}$

$\Rightarrow \frac{x^{2} + 1}{x + 3} + \frac{x^{2} + 3}{x^{2} - 9} = \frac{x^{2} + 1}{x + 3} + \frac{x^{2} + 3}{(x - 3) (x + 3)}$

$\Rightarrow \frac{(x^{2} + 1) (x - 3) + x^{2} + 3}{(x - 3) (x + 3)}$

$\Rightarrow \frac{x^{3} - 3 x^{2} + x - 3 + x^{2} + 3}{(x - 3) (x + 3)}$

$\Rightarrow \frac{x^{3} - 2 x^{2} + x}{(x - 3) (x + 3)}$
$\Rightarrow \frac{x^{3} - 2 x^{2} + x}{(x^{2} - 9)}$

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Similar questions

(x+1) is a factor of the polynomial
(a) $x^{3} + x^{2} - x + 1$
(b) $x^{3} + 2 x^{2} - x - 2$
(c) $x^{3} + 2 x^{2} - x + 2$
(d) $x^{4} + x^{3} + x^{2} + 1$

Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

Q. Simplify:

\frac{(2 x^{2})}{x^{2} - 9} + \frac{x + 15}{9 - x^{2}}

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

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The sum of the reciprocals of x+3x2+1 and x2−9x2+3 is

The correct option is B x3−2x2+xx2−9Consider the sum of the reciprocals of , x+3x2+1 and x2−9x2+3 ⇒x2+1x+3+x2+3x2−9=x2+1x+3+x2+3(x−3)(x+3) ⇒(x2+1)(x−3)+x2+3(x−3)(x+3) ⇒x3−3x2+x−3+x2+3(x−3)(x+3) ⇒x3−2x2+x(x−3)(x+3) ⇒x3−2x2+x(x2−9)

The sum of the reciprocals of $\frac{x + 3}{x^{2} + 1}$ and $\frac{x^{2} - 9}{x^{2} + 3}$ is