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simplify: (x^2-8x+16)/(x^2-x-12)÷(4x-x^2)/(2x)

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swavers | Student, Grade 11 | eNoter

Posted February 13, 2011 at 7:13 AM via web

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simplify: (x^2-8x+16)/(x^2-x-12)÷(4x-x^2)/(2x)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 13, 2011 at 11:17 AM (Answer #1)

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We have to simplify: (x^2-8x+16)/(x^2-x-12)÷(4x-x^2)/(2x)

Now, x^2 - 8x + 16 = (x - 4)^2

x^2 - x - 12 = x^2 - 4x + 3x - 12

=> x(x - 4) + 3(x - 4) = (x + 3)(x - 4)

4x - x^2 = x(4 - x)

[(x^2-8x+16)/(x^2-x-12)]/[(4x-x^2)/(2x)]

=> [(x - 4)^2/(x + 3)(x - 4)]/[x(4 - x)/2x]

=> [(x - 4)/(x + 3)]/[(4 - x)/2]

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

=> -2/ (x + 3)

The simplified form is -2/ (x + 3)

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