Solve 1/8.5=1/90+1/x

$$\frac{ 1 }{ 8.5 } = \frac{ 1 }{ 90 } + \frac{ 1 }{ x }$$

Solve for x

$$x = \frac{1530}{163} = 9\frac{63}{163} \approx 9.386503067$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 90x, the least common multiple of 90,x.

$$90x\times \frac{1}{8.5}=90x\times \frac{1}{90}+90$$

Expand \frac{1}{8.5} by multiplying both numerator and the denominator by 10.

$$90x\times \frac{10}{85}=90x\times \frac{1}{90}+90$$

Reduce the fraction \frac{10}{85} to lowest terms by extracting and canceling out 5.

$$90x\times \frac{2}{17}=90x\times \frac{1}{90}+90$$

Express 90\times \frac{2}{17} as a single fraction.

$$\frac{90\times 2}{17}x=90x\times \frac{1}{90}+90$$

Multiply 90 and 2 to get 180.

$$\frac{180}{17}x=90x\times \frac{1}{90}+90$$

Cancel out 90 and 90.

$$\frac{180}{17}x=x+90$$

Subtract x from both sides.

$$\frac{180}{17}x-x=90$$

Combine \frac{180}{17}x and -x to get \frac{163}{17}x.

$$\frac{163}{17}x=90$$

Multiply both sides by \frac{17}{163}, the reciprocal of \frac{163}{17}.

$$x=90\times \frac{17}{163}$$

Express 90\times \frac{17}{163} as a single fraction.

$$x=\frac{90\times 17}{163}$$

Multiply 90 and 17 to get 1530.

$$x=\frac{1530}{163}$$