Simplify 9 x2-12 x-4-4 x2-27 x-7-12 x2-5 x-2-16 x2-1

The correct option is D (3x+2)/(x 7)9x^2+12x+4/4x^2 27x 7÷12x^2+5x 2/16x^2 1= (3x+2)(3x+2)/(4x+1)(x 7)÷(3x+2)(4x 1)/(4x+1)(4x 1) = (3x+2)(3x+2)/(4x+1)(x 7)×(4 ...

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Byju's Answer

Standard X

Mathematics

Division of Rational Expressions

Simplify 9 x2...

Question

Simplify $\frac{9 x^{2} + 12 x + 4}{4 x^{2} - 27 x - 7} \div \frac{12 x^{2} + 5 x - 2}{16 x^{2} - 1} .$

\frac{(3 x + 2)}{(x + 7)}

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\frac{(3 x - 2)}{(x + 7)}

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\frac{(3 x + 2)}{(x - 7)}

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\frac{(3 x - 2)}{(x - 7)}

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Solution

The correct option is C $\frac{(3 x + 2)}{(x - 7)}$
$\frac{9 x^{2} + 12 x + 4}{4 x^{2} - 27 x - 7} \div \frac{12 x^{2} + 5 x - 2}{16 x^{2} - 1} = \frac{(3 x + 2) (3 x + 2)}{(4 x + 1) (x - 7)} \div \frac{(3 x + 2) (4 x - 1)}{(4 x + 1) (4 x - 1)}$

$= \frac{(3 x + 2) (3 x + 2)}{(4 x + 1) (x - 7)} \times \frac{(4 x + 1) (4 x - 1)}{(3 x + 2) (4 x - 1)}$

$= \frac{(3 x + 2)}{(x - 7)}$

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Q. If

(2 x^{2} - 3 x + 1) (2 x^{2} + 5 x + 1) = 9 x^{2}

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(i)

\frac{5 x + 20}{7 x + 28}

(ii)

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(iii)

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Q. Simplify:

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Simplify 9x2+12x+44x2−27x−7÷12x2+5x−216x2−1.

The correct option is C (3x+2)(x−7)9x2+12x+44x2−27x−7÷12x2+5x−216x2−1=(3x+2)(3x+2)(4x+1)(x−7)÷(3x+2)(4x−1)(4x+1)(4x−1) =(3x+2)(3x+2)(4x+1)(x−7)×(4x+1)(4x−1)(3x+2)(4x−1) =(3x+2)(x−7)

Simplify $\frac{9 x^{2} + 12 x + 4}{4 x^{2} - 27 x - 7} \div \frac{12 x^{2} + 5 x - 2}{16 x^{2} - 1} .$