Solve 510/x(x-2)+4/x=5/x-2

$$5 \frac { 10 } { x ( x - 2 ) } + \frac { 4 } { x } = \frac { 5 } { x - 2 }$$

Solve for x

$$x=42$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by x\left(x-2\right), the least common multiple of x\left(x-2\right),x,x-2.

$$5\times 10+\left(x-2\right)\times 4=x\times 5$$

Multiply 5 and 10 to get 50.

$$50+\left(x-2\right)\times 4=x\times 5$$

Use the distributive property to multiply x-2 by 4.

$$50+4x-8=x\times 5$$

Subtract 8 from 50 to get 42.

$$42+4x=x\times 5$$

Subtract x\times 5 from both sides.

$$42+4x-x\times 5=0$$

Combine 4x and -x\times 5 to get -x.

$$42-x=0$$

Subtract 42 from both sides. Anything subtracted from zero gives its negation.

$$-x=-42$$

Multiply both sides by -1.

$$x=42$$