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Simplify: `(2x^2-14x+20)/(7x-2x^2-6)`

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spock3 | Student, Undergraduate | (Level 2) Honors

Posted May 2, 2012 at 1:26 PM via web

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Simplify: `(2x^2-14x+20)/(7x-2x^2-6)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 2, 2012 at 2:08 PM (Answer #1)

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To simplify `(2x^2-14x+20)/(7x-2x^2-6)` factorize the numerator and denominator.

2x^2-14x+20

= 2x^2-10x-4x+20

= 2x(x - 5) - 4(x- 5)

= (2x - 4)(x - 5)

7x-2x^2-6

= -2x^2 + 4x + 3x - 6

= -2x(x - 2) + 3(x - 2)

= (-2x + 3)(x - 2)

`(2x^2-14x+20)/(7x-2x^2-6)`

=> `((2x - 4)(x - 5))/((-2x + 3)(x - 2))`

=> `(2x - 10)/(3 - 2x)`

The simplified form of `(2x^2-14x+20)/(7x-2x^2-6) = (2x - 10)/(3 - 2x)`

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