Solve 2,5+x/x=5,8/5,3

$$\frac { 2,5 + x } { x } = \frac { 5,8 } { 5,3 }$$

Solve for x

$$x=26,5$$

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.

$$2,5+x=x\times \frac{5,8}{5,3}$$

Expand \frac{5,8}{5,3} by multiplying both numerator and the denominator by 10.

$$2,5+x=x\times \frac{58}{53}$$

Subtract x\times \frac{58}{53} from both sides.

$$2,5+x-x\times \frac{58}{53}=0$$

Combine x and -x\times \frac{58}{53} to get -\frac{5}{53}x.

$$2,5-\frac{5}{53}x=0$$

Subtract 2,5 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{53}x=-2,5$$

Multiply both sides by -\frac{53}{5}, the reciprocal of -\frac{5}{53}.

$$x=-2,5\left(-\frac{53}{5}\right)$$

Convert decimal number -2,5 to fraction -\frac{25}{10}. Reduce the fraction -\frac{25}{10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{5}{2}\left(-\frac{53}{5}\right)$$

Multiply -\frac{5}{2} times -\frac{53}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-53\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-5\left(-53\right)}{2\times 5}.

$$x=\frac{265}{10}$$

Reduce the fraction \frac{265}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{53}{2}$$