What is the answer to 1/x+6= 5/(sqrt(x)) ?

The answer to 1/x+6= 5/(sqrt(x)) is x= 1/9 ,x= 1/4

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1/x+6= 5/(sqrt(x))

\frac{1}{x} + 6 = \frac{5}{x}

x = \frac{1}{9}, x = \frac{1}{4}

Decimal Notation

x = 0.11111 \dots, x = 0.25

Solution steps

\frac{1}{x} + 6 = \frac{5}{x}

Find Least Common Multiplier of

x, x : x x

Multiply by LCM=

x x

\frac{1}{x} x x + 6 x x = \frac{5}{x} x x

Simplify

x + 6 x x = 5 x

Factor

x + 6 x x : x (6 x + 1)

x (6 x + 1) = 5 x

Square both sides:

36 x^{3} + 12 x^{2} + x = 25 x^{2}

36 x^{3} + 12 x^{2} + x = 25 x^{2}

Solve

36 x^{3} + 12 x^{2} + x = 25 x^{2} : x = 0, x = \frac{1}{9}, x = \frac{1}{4}

x = 0, x = \frac{1}{9}, x = \frac{1}{4}

Verify Solutions:

x = 0

False

, x = \frac{1}{9}

True

, x = \frac{1}{4}

True

The solutions are

x = \frac{1}{9}, x = \frac{1}{4}

x - 6 = x - 3

2 x - 6 x + 2 + 1 = 0

x - 5 = 2 x - 6 - 2

6 x - 5 x - 6 = 0

f, f (x - 3) = x + 3 + 3

What is the answer to 1/x+6= 5/(sqrt(x)) ?
The answer to 1/x+6= 5/(sqrt(x)) is x= 1/9 ,x= 1/4
Solve for x: 1/x+6= 5/(sqrt(x))
The solution is x= 1/9 ,x= 1/4