Solve 90/x+90-40/x+40=02

$$\frac{ 90 }{ x+90 } - \frac{ 40 }{ x+40 } =02$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -90,-40 since division by zero is not defined. Multiply both sides of the equation by \left(x+40\right)\left(x+90\right), the least common multiple of x+90,x+40.

$$\left(x+40\right)\times 90-\left(x+90\right)\times 40=0\times 2\left(x+40\right)\left(x+90\right)$$

Use the distributive property to multiply x+40 by 90.

$$90x+3600-\left(x+90\right)\times 40=0\times 2\left(x+40\right)\left(x+90\right)$$

Use the distributive property to multiply x+90 by 40.

$$90x+3600-\left(40x+3600\right)=0\times 2\left(x+40\right)\left(x+90\right)$$

To find the opposite of 40x+3600, find the opposite of each term.

$$90x+3600-40x-3600=0\times 2\left(x+40\right)\left(x+90\right)$$

Combine 90x and -40x to get 50x.

$$50x+3600-3600=0\times 2\left(x+40\right)\left(x+90\right)$$

Subtract 3600 from 3600 to get 0.

$$50x=0\times 2\left(x+40\right)\left(x+90\right)$$

Multiply 0 and 2 to get 0.

$$50x=0\left(x+40\right)\left(x+90\right)$$

Anything times zero gives zero.

$$50x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 50 is not equal to 0, x must be equal to 0.

$$x=0$$