Solve 2-5/2x=2x/x+1

$$2- \frac{ 5 }{ 2x } = \frac{ 2x }{ x+1 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+1\right), the least common multiple of 2x,x+1.

$$2x\left(x+1\right)\times 2-\left(x+1\right)\times 5=2x\times 2x$$

Multiply 2x and 2x to get \left(2x\right)^{2}.

$$2x\left(x+1\right)\times 2-\left(x+1\right)\times 5=\left(2x\right)^{2}$$

Use the distributive property to multiply 2x by x+1.

$$\left(2x^{2}+2x\right)\times 2-\left(x+1\right)\times 5=\left(2x\right)^{2}$$

Use the distributive property to multiply 2x^{2}+2x by 2.

$$4x^{2}+4x-\left(x+1\right)\times 5=\left(2x\right)^{2}$$

Use the distributive property to multiply x+1 by 5.

$$4x^{2}+4x-\left(5x+5\right)=\left(2x\right)^{2}$$

To find the opposite of 5x+5, find the opposite of each term.

$$4x^{2}+4x-5x-5=\left(2x\right)^{2}$$

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

$$4x^{2}-x-5=\left(2x\right)^{2}$$

Expand \left(2x\right)^{2}.

$$4x^{2}-x-5=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-x-5=4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}-x-5-4x^{2}=0$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-x-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$-x=5$$

Multiply both sides by -1.

$$x=-5$$