Evaluate 6 x2-x-2-8 x2-6 x-1-12 x2-13 x-4-12 x2-25 x-12

The correct option is C 3x 2/4x 36x^2 x 2/8x^2 + 6x + 1×12x^2 13x 4/12x^2 25x + 12 = (3x 2)(2x+1)/(2x+1)(4x+1)×(4x+1)(3x 4)/(4x 3)(3x 4) = (3x 2)(2x ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Rational Expressions

Evaluate 6 x2...

Question

Evaluate $\frac{6 x^{2} - x - 2}{8 x^{2} + 6 x + 1} \times \frac{12 x^{2} - 13 x - 4}{12 x^{2} - 25 x + 12}$

\frac{3 x - 2}{4 x - 3}

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\frac{3 x + 2}{4 x + 3}

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None of the above

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Solution

The correct option is A $\frac{3 x - 2}{4 x - 3}$
$\frac{6 x^{2} - x - 2}{8 x^{2} + 6 x + 1} \times \frac{12 x^{2} - 13 x - 4}{12 x^{2} - 25 x + 12}$

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

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

Cancelling $(2 x + 1) (4 x + 1) (3 x - 4)$ from numerator and denominator

= $\frac{3 x - 2}{4 x - 3}$

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Similar questions

Q. Solve for

x

\frac{6 x^{2} + 13 x - 4}{2 x + 5} = \frac{12 x^{2} + 5 x - 2}{4 x + 3}

Q. Solve the folowing equation:

\frac{6 x^{2} + 13 x - 4}{2 x + 5} = \frac{12 x^{2} + 5 x - 2}{4 x + 3}

12(x²+7)²-8(x²+7)²(2x-1)-15(2x-1)²

Factories:

$12 x^{2} - 25 x + 12$

Q. Factorise:

12 (x^{2} + 7 x)^{2} - 8 (x^{2} + 7 x) (2 x - 1) - 15 (2 x - 1)^{2}

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Evaluate 6x2−x−28x2+6x+1×12x2−13x−412x2−25x+12

The correct option is A 3x−24x−36x2−x−28x2+6x+1×12x2−13x−412x2−25x+12 = (3x−2)(2x+1)(2x+1)(4x+1)×(4x+1)(3x−4)(4x−3)(3x−4) = (3x−2)(2x+1)(4x+1)(3x−4)(2x+1)(4x+1)(4x−3)(3x−4) Cancelling (2x+1)(4x+1)(3x−4) from numerator and denominator = 3x−24x−3

Evaluate $\frac{6 x^{2} - x - 2}{8 x^{2} + 6 x + 1} \times \frac{12 x^{2} - 13 x - 4}{12 x^{2} - 25 x + 12}$