The simplest form of x3-1-x2-1 isA- x2-1 -x-1B- x2-x-1C- x2-2 x-1 -x-1D- x2-x-1 -x-1

The correct option is D (x2 + x + 1)/(x+1) (x^3 – 1)/(x^2 – 1) = [(x – 1)(x^2 + x + 1)]/[(x 1)(x+1)] = [(x^2 + x + 1)]/(x+1) ...

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Standard X

Mathematics

Rational Expression

The simplest ...

Question

The simplest form of $\frac{(x^{3} - 1)}{(x^{2} - 1)}$ is

(x² + 1)/(x+1)

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(x² + x + 1)

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(x² + 2x + 1)/(x+1)

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(x² + x + 1)/(x+1)

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Solution

The correct option is D
(x² + x + 1)/(x+1)

$(x^{3} - 1) / (x^{2} - 1)$ = $\frac{[(x - 1) (x^{2} + x + 1)]}{[(x - 1) (x + 1)]}$

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

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Similar questions

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

Q. Find the H.C.F. of

(x^{2} + x + 1)

and

(x^{4} + x^{2} + 1)

by using the division method.

\int \frac{d x}{(x + 1) \sqrt{x^{2} - 1}} =

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

Q. What is the quotient obtained when

x^{3} + x^{2} - 5 x + 3

is divided by

x^{2} + 2 x - 3

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The simplest form of (x3–1)(x2–1) is

The correct option is D (x2 + x + 1)/(x+1) (x3–1)/(x2–1) = [(x–1)(x2+x+1)][(x−1)(x+1)] = [(x2+x+1)](x+1)

The simplest form of $\frac{(x^{3} - 1)}{(x^{2} - 1)}$ is

The correct option is D
(x² + x + 1)/(x+1)

$(x^{3} - 1) / (x^{2} - 1)$ = $\frac{[(x - 1) (x^{2} + x + 1)]}{[(x - 1) (x + 1)]}$

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