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3 years ago

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svetoff [14.1K]3 years ago

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Find x: 3/(x-4)(x-7) + 6/(x-7)(x-13) + 15/(x-13)(x-28) - 1/x-28 = -1/20

Novay_Z [31]

The value of x in the polynomial fraction 3/((x-4)•(x-7)) + 6/((x-7)•(x-13)) + 15/((x-13)•(x-28)) - 1/(x-28) = -1/20 is x = 24

<h3>How can the polynomial with fractions be simplified to find x?</h3>

The given equation is presented as follows;

$\frac{3}{(x - 4) \cdot (x - 7) } + \frac{6}{(x - 7) \cdot (x - 13) } + +\frac{15}{(x - 13) \cdot (x - 28) } - \frac{1}{(x - 28) } = - \frac{1}{20}$

Factoring the common denominator, we have;

$\frac{3\cdot(x - 13) \cdot(x - 28) + 6 \cdot(x - 4) \cdot(x - 28) + 15 \cdot(x - 4) \cdot(x - 7) - (x - 4) \cdot (x - 7)\cdot(x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Simplifying the numerator of the right hand side using a graphing calculator, we get;

By expanding and collecting, the terms of the numerator gives;

-(x³ - 48•x + 651•x - 2548)

Given that the terms of the numerator have several factors in common, we get;

-(x³ - 48•x + 651•x - 2548) = -(x-7)•(x-28)•(x-13)

Which gives;

$\frac{-(x - 7) \cdot(x - 28)\cdot (x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Which gives;

$\frac{-1}{(x - 4)} + = - \frac{1}{20}$

x - 4 = 20

Therefore;

x = 20 + 4 = 24

Learn more about polynomials with fractions here:

brainly.com/question/12262414

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In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all i

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Barry got a samll sandwich for lunch and ate 1/2 of his sandwich. Jonah got a large sandwich and ate 1/2 of his sandwich. Did Jo

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Write an equation that gives the proportional relationship of the graph.A) y = 14xB) y = 3xC) y = 4xD) y = 12x

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