Solve 30=1/frac{1{90}+1/x}

$$30= \frac{ 1 }{ \frac{ 1 }{ 90 } + \frac{ 1 }{ x } }$$

Solve for x

$$x=45$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 90 and x is 90x. Multiply \frac{1}{90} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{90}{90}.

$$30=\frac{1}{\frac{x}{90x}+\frac{90}{90x}}$$

Since \frac{x}{90x} and \frac{90}{90x} have the same denominator, add them by adding their numerators.

$$30=\frac{1}{\frac{x+90}{90x}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 1 by \frac{x+90}{90x} by multiplying 1 by the reciprocal of \frac{x+90}{90x}.

$$30=\frac{90x}{x+90}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{90x}{x+90}=30$$

Variable x cannot be equal to -90 since division by zero is not defined. Multiply both sides of the equation by x+90.

$$90x=30\left(x+90\right)$$

Use the distributive property to multiply 30 by x+90.

$$90x=30x+2700$$

Subtract 30x from both sides.

$$90x-30x=2700$$

Combine 90x and -30x to get 60x.

$$60x=2700$$

Divide both sides by 60.

$$x=\frac{2700}{60}$$

Divide 2700 by 60 to get 45.

$$x=45$$