Find the sum of x-1-x-2 and x2-1-x2-1-

The correct option is D 2x^3 + 3x^2 1/x^3 + 2x^2 + x + 2x+1/x+2+ x^2 1/x^2+1 nbsp; = (x+1)(x^2+1) + (x^2 1)(x+2)/(x+2)(x^2+1) = 2x^3 + 3x^2 1/x^3 + 2x^2 ...

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Byju's Answer

Standard X

Mathematics

Addition of Rational Expressions

Find the sum ...

Question

Find the sum of $\frac{x + 1}{x + 2}$ and $\frac{x^{2} - 1}{x^{2} + 1} .$

\frac{2 x^{3} + 3 x^{2} + 1}{x^{3} + 2 x^{2} + x + 2}

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\frac{2 x^{3} - 3 x^{2} - 1}{x^{3} - 2 x^{2} - x + 2}

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\frac{3 x^{3} + 3 x^{2} - 1}{2 x^{3} + 2 x^{2} + x + 2}

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\frac{2 x^{3} + 3 x^{2} - 1}{x^{3} + 2 x^{2} + x + 2}

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Solution

The correct option is D $\frac{2 x^{3} + 3 x^{2} - 1}{x^{3} + 2 x^{2} + x + 2}$
$\frac{x + 1}{x + 2} + \frac{x^{2} - 1}{x^{2} + 1}$

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

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

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Find the sum of x+1x+2 and x2−1x2+1.

The correct option is D 2x3+3x2−1x3+2x2+x+2x+1x+2+x2−1x2+1 = (x+1)(x2+1)+(x2−1)(x+2)(x+2)(x2+1) = 2x3+3x2−1x3+2x2+x+2

Find the sum of $\frac{x + 1}{x + 2}$ and $\frac{x^{2} - 1}{x^{2} + 1} .$

The correct option is D $\frac{2 x^{3} + 3 x^{2} - 1}{x^{3} + 2 x^{2} + x + 2}$
$\frac{x + 1}{x + 2} + \frac{x^{2} - 1}{x^{2} + 1}$

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

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