Solve 0.482=0.288x/x-1+0.5/x-1

$$0.482 = \frac { 0.288 x } { x - 1 } + \frac { 0.5 } { x - 1 }$$

Solve for x

$$x = \frac{491}{97} = 5\frac{6}{97} \approx 5.06185567$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$0.482\left(x-1\right)=0.288x+0.5$$

Use the distributive property to multiply 0.482 by x-1.

$$0.482x-0.482=0.288x+0.5$$

Subtract 0.288x from both sides.

$$0.482x-0.482-0.288x=0.5$$

Combine 0.482x and -0.288x to get 0.194x.

$$0.194x-0.482=0.5$$

Add 0.482 to both sides.

$$0.194x=0.5+0.482$$

Add 0.5 and 0.482 to get 0.982.

$$0.194x=0.982$$

Divide both sides by 0.194.

$$x=\frac{0.982}{0.194}$$

Expand \frac{0.982}{0.194} by multiplying both numerator and the denominator by 1000.

$$x=\frac{982}{194}$$

Reduce the fraction \frac{982}{194} to lowest terms by extracting and canceling out 2.

$$x=\frac{491}{97}$$