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

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:

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

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