Solve 10/x-05=12/x+2

$$\frac { 10 } { x } - 05 = \frac { 12 } { x + 2 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0 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,x+2.

$$\left(x+2\right)\times 10-0\times 5x\left(x+2\right)=x\times 12$$

Use the distributive property to multiply x+2 by 10.

$$10x+20-0\times 5x\left(x+2\right)=x\times 12$$

Multiply 0 and 5 to get 0.

$$10x+20-0x\left(x+2\right)=x\times 12$$

Anything times zero gives zero.

$$10x+20-0=x\times 12$$

Subtract x\times 12 from both sides.

$$10x+20-0-x\times 12=0$$

Reorder the terms.

$$10x+20-12x=0$$

Combine 10x and -12x to get -2x.

$$-2x+20=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-20$$

Divide both sides by -2.

$$x=\frac{-20}{-2}$$

Divide -20 by -2 to get 10.

$$x=10$$