Subtract the rational expression- x2-4x-4x-2-x-2x-2

The correct option is B x^2 x 6x 2 Here, x^2+4x+4x+2 x+2x 2 Factor of x^2+4x+4 = (x+2)(x+2) = (x+2)(x+2)x+2 x+2x 2 Cross multiplying, ...

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Standard X

Mathematics

Addition of Rational Expressions

Subtract the ...

Question

Subtract the rational expression: $\frac{x^{2} + 4 x + 4}{x + 2} - \frac{x + 2}{x - 2}$

\frac{x - 6}{x - 2}

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\frac{x + 6}{x - 2}

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\frac{x^{2} - x - 6}{x - 2}

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\frac{x^{2} - x - 6}{x + 2}

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Solution

The correct option is B $\frac{x^{2} - x - 6}{x - 2}$
Here, $\frac{x^{2} + 4 x + 4}{x + 2} - \frac{x + 2}{x - 2}$

Factor of $x^{2} + 4 x + 4 = (x + 2) (x + 2)$

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

Cross multiplying, we get

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

$=$ $\frac{x^{2} - 4 - x - 2}{x - 2}$

$=$ $\frac{x^{2} - x - 6}{x - 2}$

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Subtract the rational expression: x2+4x+4x+2−x+2x−2

The correct option is B x2−x−6x−2Here, x2+4x+4x+2−x+2x−2Factor of x2+4x+4=(x+2)(x+2)= (x+2)(x+2)x+2−x+2x−2Cross multiplying, we get= (x+2)(x−2)−(x+2)x−2= x2−4−x−2x−2= x2−x−6x−2

Subtract the rational expression: $\frac{x^{2} + 4 x + 4}{x + 2} - \frac{x + 2}{x - 2}$