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22 December, 09:31

Solve 3/3x + 1/x+4 = 10/7x solve for x

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  1. 22 December, 09:51
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    x = 14/3 + sqrt (217) / 3 or x = 14/3 - sqrt (217) / 3

    Step-by-step explanation:

    Solve for x:

    x + 4 + 1/x = (10 x) / 7

    Bring x + 4 + 1/x together using the common denominator x:

    (x^2 + 4 x + 1) / x = (10 x) / 7

    Cross multiply:

    7 (x^2 + 4 x + 1) = 10 x^2

    Expand out terms of the left hand side:

    7 x^2 + 28 x + 7 = 10 x^2

    Subtract 10 x^2 from both sides:

    -3 x^2 + 28 x + 7 = 0

    Divide both sides by - 3:

    x^2 - (28 x) / 3 - 7/3 = 0

    Add 7/3 to both sides:

    x^2 - (28 x) / 3 = 7/3

    Add 196/9 to both sides:

    x^2 - (28 x) / 3 + 196/9 = 217/9

    Write the left hand side as a square:

    (x - 14/3) ^2 = 217/9

    Take the square root of both sides:

    x - 14/3 = sqrt (217) / 3 or x - 14/3 = - sqrt (217) / 3

    Add 14/3 to both sides:

    x = 14/3 + sqrt (217) / 3 or x - 14/3 = - sqrt (217) / 3

    Add 14/3 to both sides:

    Answer: x = 14/3 + sqrt (217) / 3 or x = 14/3 - sqrt (217) / 3
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