Simplify- 1 - 2x - x21 - x3-1 - x - x21 - x

1 2x + x^21 x^3×1 + x + x^21 + x = 1 x x+x^2(1)^3 (x)^3×1+x+x^21 + x = 1(1 x) x(1 x)(1 x){(1)^2 + (1) × (x) + (x)^2 }×(1 + x +x^2)1 + x = (1 x)(1 x)(1 x)(1+ ...

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Byju's Answer

Standard VIII

Mathematics

Factorization of a Quadratic Trinomial

Simplify: 1 -...

Question

Simplify: $\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}$

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Solution

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

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Simplify: 1−2x+x21−x3×1+x+x21+x

1−2x+x21−x3×1+x+x21+x =1−x−x+x2(1)3(x)3×1+x+x21+x =1(1−x)−x(1−x)(1−x){(1)2+(1)×(x)+(x)2}×(1+x+x2)1+x =(1−x)(1−x)(1−x)(1+x+x2)×(1+x+x2)(1+x) =1−x1+x

Simplify: $\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}$