Express 6 x2-21 x-12-54 x2-45 x-9 in its lowest form

The correct option is B (x 4)/3(3x+1)Factor the numerator: 6x2 21x 12 = 3(2x2 7x 4) = 3(x 4)(2x + 1) Factor the denominator: 54x2 +45x + 9 = 9(6x2 + ...

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Byju's Answer

Standard X

Mathematics

Division of Rational Expressions

Express 6 x2-...

Question

Express $\frac{6 x^{2} - 21 x - 12}{54 x^{2} + 45 x + 9}$ in its lowest form.

\frac{(2 x - 1)}{9 (3 x + 1)}

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\frac{(x - 4)}{3 (3 x + 1)}

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\frac{(2 x + 1)}{3 (3 x + 1)}

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\frac{(x - 4)}{3 (2 x + 1)}

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Solution

The correct option is B $\frac{(x - 4)}{3 (3 x + 1)}$
Factor the numerator: 6x² -21x - 12 = 3(2x² - 7x - 4) = 3(x - 4)(2x + 1)

Factor the denominator: 54x² +45x + 9 = 9(6x² + 5x + 1) = 9(3x + 1)(2x + 1).

$∴ \frac{6 x^{2} - 21 x - 12}{54 x^{2} + 45 x + 9} = \frac{3 (x - 4) (2 x + 1)}{9 (3 x + 1) (2 x + 1)}$

Cancelling out common factors,

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

Suggest Corrections

Express 6x2−21x−1254x2+45x+9 in its lowest form.

The correct option is B (x−4)3(3x+1)Factor the numerator: 6x2 -21x - 12 = 3(2x2 - 7x - 4) = 3(x - 4)(2x + 1) Factor the denominator: 54x2 +45x + 9 = 9(6x2 + 5x + 1) = 9(3x + 1)(2x + 1). ∴6x2−21x−1254x2+45x+9=3(x−4)(2x+1)9(3x+1)(2x+1) Cancelling out common factors, = (x−4)3(3x+1)

Express $\frac{6 x^{2} - 21 x - 12}{54 x^{2} + 45 x + 9}$ in its lowest form.