Solve 1/x=.99/250+0.99/900+frac{0.90/250}{frac{1}{250}+frac{1}{900}+frac{1}{250}}

$$\frac{ 1 }{ x } = \frac{ \frac{ .99 }{ 250 } + \frac{ 0.99 }{ 900 } + \frac{ 0.90 }{ 250 } }{ \frac{ 1 }{ 250 } + \frac{ 1 }{ 900 } + \frac{ 1 }{ 250 } }$$

Solve for x

$$x = \frac{4100}{3897} = 1\frac{203}{3897} \approx 1.052091352$$

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 x.

$$1=\frac{4500}{41}x\left(\frac{0.99}{250}+\frac{0.99}{900}+\frac{0.9}{250}\right)$$

Expand \frac{0.99}{250} by multiplying both numerator and the denominator by 100.

$$1=\frac{4500}{41}x\left(\frac{99}{25000}+\frac{0.99}{900}+\frac{0.9}{250}\right)$$

Expand \frac{0.99}{900} by multiplying both numerator and the denominator by 100.

$$1=\frac{4500}{41}x\left(\frac{99}{25000}+\frac{99}{90000}+\frac{0.9}{250}\right)$$

Reduce the fraction \frac{99}{90000} to lowest terms by extracting and canceling out 9.

$$1=\frac{4500}{41}x\left(\frac{99}{25000}+\frac{11}{10000}+\frac{0.9}{250}\right)$$

Least common multiple of 25000 and 10000 is 50000. Convert \frac{99}{25000} and \frac{11}{10000} to fractions with denominator 50000.

$$1=\frac{4500}{41}x\left(\frac{198}{50000}+\frac{55}{50000}+\frac{0.9}{250}\right)$$

Since \frac{198}{50000} and \frac{55}{50000} have the same denominator, add them by adding their numerators.

$$1=\frac{4500}{41}x\left(\frac{198+55}{50000}+\frac{0.9}{250}\right)$$

Add 198 and 55 to get 253.

$$1=\frac{4500}{41}x\left(\frac{253}{50000}+\frac{0.9}{250}\right)$$

Expand \frac{0.9}{250} by multiplying both numerator and the denominator by 10.

$$1=\frac{4500}{41}x\left(\frac{253}{50000}+\frac{9}{2500}\right)$$

Least common multiple of 50000 and 2500 is 50000. Convert \frac{253}{50000} and \frac{9}{2500} to fractions with denominator 50000.

$$1=\frac{4500}{41}x\left(\frac{253}{50000}+\frac{180}{50000}\right)$$

Since \frac{253}{50000} and \frac{180}{50000} have the same denominator, add them by adding their numerators.

$$1=\frac{4500}{41}x\times \frac{253+180}{50000}$$

Add 253 and 180 to get 433.

$$1=\frac{4500}{41}x\times \frac{433}{50000}$$

Multiply \frac{4500}{41} times \frac{433}{50000} by multiplying numerator times numerator and denominator times denominator.

$$1=\frac{4500\times 433}{41\times 50000}x$$

Do the multiplications in the fraction \frac{4500\times 433}{41\times 50000}.

$$1=\frac{1948500}{2050000}x$$

Reduce the fraction \frac{1948500}{2050000} to lowest terms by extracting and canceling out 500.

$$1=\frac{3897}{4100}x$$

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

$$\frac{3897}{4100}x=1$$

Multiply both sides by \frac{4100}{3897}, the reciprocal of \frac{3897}{4100}.

$$x=1\times \frac{4100}{3897}$$

Multiply 1 and \frac{4100}{3897} to get \frac{4100}{3897}.

$$x=\frac{4100}{3897}$$