What is the answer to (-1)/(5-sqrt(1/5*x+1))= 17/10 ?

The answer to (-1)/(5-sqrt(1/5*x+1))= 17/10 is x= 43680/289

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(-1)/(5-sqrt(1/5*x+1))= 17/10

\frac{- 1}{5 - \frac{1}{5} \cdot x + 1} = \frac{17}{10}

x = \frac{43680}{289}

Solution steps

\frac{- 1}{5 - \frac{1}{5} x + 1} = \frac{17}{10}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(- 1) \cdot 10 = (5 - \frac{1}{5} x + 1) \cdot 17

Expand

(5 - \frac{1}{5} x + 1) \cdot 17 : 85 - 17 \frac{1}{5} x + 1

(- 1) \cdot 10 = 85 - 17 \frac{1}{5} x + 1

Switch sides

85 - 17 \frac{1}{5} x + 1 = (- 1) \cdot 10

Remove parentheses:

(- a) = - a

85 - 17 \frac{1}{5} x + 1 = - 1 \cdot 10

Multiply the numbers:

1 \cdot 10 = 10

85 - 17 \frac{1}{5} x + 1 = - 10

Move

85

to the right side

- 17 \frac{1}{5} x + 1 = - 95

Divide both sides by

- 17

\frac{1}{5} x + 1 = \frac{95}{17}

Square both sides:

\frac{1}{5} x + 1 = \frac{9025}{289}

\frac{1}{5} x + 1 = \frac{9025}{289}

Solve

\frac{1}{5} x + 1 = \frac{9025}{289} : x = \frac{43680}{289}

x = \frac{43680}{289}

Verify Solutions:

x = \frac{43680}{289}

True

The solution is

x = \frac{43680}{289}

x + 9 - 5 = 4

x - 1 = 2

x - 1 = 8

x + x - x = 1

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

What is the answer to (-1)/(5-sqrt(1/5*x+1))= 17/10 ?
The answer to (-1)/(5-sqrt(1/5*x+1))= 17/10 is x= 43680/289
Solve for x: (-1)/(5-sqrt(1/5*x+1))= 17/10
The solution is x= 43680/289