Solve 600/512=345+26.8/345-x

$$\frac{ 600 }{ 512 } = \frac{ 345+26.8 }{ 345-x }$$

Solve for x

$$x = \frac{10399}{375} = 27\frac{274}{375} \approx 27.730666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to 345 since division by zero is not defined. Multiply both sides of the equation by 512\left(x-345\right), the least common multiple of 512,345-x.

$$\left(x-345\right)\times 600=-512\left(345+26.8\right)$$

Use the distributive property to multiply x-345 by 600.

$$600x-207000=-512\left(345+26.8\right)$$

Add 345 and 26.8 to get 371.8.

$$600x-207000=-512\times 371.8$$

Multiply -512 and 371.8 to get -190361.6.

$$600x-207000=-190361.6$$

Add 207000 to both sides.

$$600x=-190361.6+207000$$

Add -190361.6 and 207000 to get 16638.4.

$$600x=16638.4$$

Divide both sides by 600.

$$x=\frac{16638.4}{600}$$

Expand \frac{16638.4}{600} by multiplying both numerator and the denominator by 10.

$$x=\frac{166384}{6000}$$

Reduce the fraction \frac{166384}{6000} to lowest terms by extracting and canceling out 16.

$$x=\frac{10399}{375}$$