Solve 5/2x-5-4/x-2=0

$$\frac { 5 } { 2 x - 5 } - \frac { 4 } { x - 2 } = 0$$

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,\frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(2x-5\right), the least common multiple of 2x-5,x-2.

$$\left(x-2\right)\times 5-\left(2x-5\right)\times 4=0$$

Use the distributive property to multiply x-2 by 5.

$$5x-10-\left(2x-5\right)\times 4=0$$

Use the distributive property to multiply 2x-5 by 4.

$$5x-10-\left(8x-20\right)=0$$

To find the opposite of 8x-20, find the opposite of each term.

$$5x-10-8x+20=0$$

Combine 5x and -8x to get -3x.

$$-3x-10+20=0$$

Add -10 and 20 to get 10.

$$-3x+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-10$$

Divide both sides by -3.

$$x=\frac{-10}{-3}$$

Fraction \frac{-10}{-3} can be simplified to \frac{10}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{10}{3}$$