Solve x^2+6/2x-10-x/2=x/x-5

$$\frac{ { x }^{ 2 } +6 }{ 2x-10 } - \frac{ x }{ 2 } = \frac{ x }{ x-5 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-5\right), the least common multiple of 2x-10,2,x-5.

$$x^{2}+6-\left(x-5\right)x=2x$$

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

$$x^{2}+6-\left(x^{2}-5x\right)=2x$$

To find the opposite of x^{2}-5x, find the opposite of each term.

$$x^{2}+6-x^{2}+5x=2x$$

Combine x^{2} and -x^{2} to get 0.

$$6+5x=2x$$

Subtract 2x from both sides.

$$6+5x-2x=0$$

Combine 5x and -2x to get 3x.

$$6+3x=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$3x=-6$$

Divide both sides by 3.

$$x=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x=-2$$