Evaluate 2 x2-5 x-3-2 x2-7 x-6-2 x2-5 x-3-2 x2-x-6

The correct option is A x 2/x+22x^2+5x 3/2x^2+7x+6÷2x^2+5x 3/2x^2 x 6 = nbsp;2x^2+5x 3/2x^2+7x+6×2x^2 x 6/2x^2+5x 3 Cancelling 2x^2+5x 3 from numerator and ...

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Byju's Answer

Standard X

Mathematics

Division of Rational Expressions

Evaluate 2 x2...

Question

Evaluate $\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 7 x - 6} \div \frac{2 x^{2} + 5 x - 3}{2 x^{2} - x - 6}$

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

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

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

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

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Solution

The correct option is A $\frac{x - 2}{x + 2}$
$\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 7 x + 6} \div \frac{2 x^{2} + 5 x - 3}{2 x^{2} - x - 6}$

= $\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 7 x + 6} \times \frac{2 x^{2} - x - 6}{2 x^{2} + 5 x - 3}$

Cancelling $2 x^{2} + 5 x - 3$ from numerator and denominator.

= $\frac{2 x^{2} - x - 6}{2 x^{2} + 7 x + 6}$

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

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

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Similar questions

Q. Evaluate

l = lim x \to 2 (\frac{1}{(x^{2} - 5 x + 5)} + \frac{1}{(2 x^{2} - 7 x + 6)})

Q. Evaluate :

l i m_{x \to 2} x^{2} + 5 x + 6

Q. Evaluate:

\int \frac{4 x + 6}{2 x^{2} + 5 x + 3} d x

l i m x \to 2 [\frac{1}{x^{2} - 5 x + 6} + \frac{1}{{2 x}^{2} - 7 x + 6}]

Q. Factorise:
(i)

12 x^{2} - 7 x - 1

(ii)

2 x^{2} + 7 x + 3

(iii)

6 x^{2} + 5 x - 6

(iv)

3 x^{2} - x - 4

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Evaluate 2x2+5x−32x2+7x−6÷2x2+5x−32x2−x−6

The correct option is A x−2x+22x2+5x−32x2+7x+6÷2x2+5x−32x2−x−6 = 2x2+5x−32x2+7x+6×2x2−x−62x2+5x−3 Cancelling 2x2+5x−3 from numerator and denominator. = 2x2−x−62x2+7x+6 = (x−2)(2x+3)(x+2)(2x+3) = x−2x+2

Evaluate $\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 7 x - 6} \div \frac{2 x^{2} + 5 x - 3}{2 x^{2} - x - 6}$