Solve -36x/-36+x=36+(-72)x/(-72)+x

$$\frac { - 36 x } { - 36 + x } = 36 + \frac { ( - 72 ) x } { ( - 72 ) + x }$$

Solve for x

$$x=24$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 36,72 since division by zero is not defined. Multiply both sides of the equation by \left(x-72\right)\left(x-36\right), the least common multiple of -36+x,-72+x.

$$\left(x-72\right)\left(-36\right)x=\left(x-72\right)\left(x-36\right)\times 36+\left(x-36\right)\left(-72\right)x$$

Use the distributive property to multiply x-72 by -36.

$$\left(-36x+2592\right)x=\left(x-72\right)\left(x-36\right)\times 36+\left(x-36\right)\left(-72\right)x$$

Use the distributive property to multiply -36x+2592 by x.

$$-36x^{2}+2592x=\left(x-72\right)\left(x-36\right)\times 36+\left(x-36\right)\left(-72\right)x$$

Use the distributive property to multiply x-72 by x-36 and combine like terms.

$$-36x^{2}+2592x=\left(x^{2}-108x+2592\right)\times 36+\left(x-36\right)\left(-72\right)x$$

Use the distributive property to multiply x^{2}-108x+2592 by 36.

$$-36x^{2}+2592x=36x^{2}-3888x+93312+\left(x-36\right)\left(-72\right)x$$

Use the distributive property to multiply x-36 by -72.

$$-36x^{2}+2592x=36x^{2}-3888x+93312+\left(-72x+2592\right)x$$

Use the distributive property to multiply -72x+2592 by x.

$$-36x^{2}+2592x=36x^{2}-3888x+93312-72x^{2}+2592x$$

Combine 36x^{2} and -72x^{2} to get -36x^{2}.

$$-36x^{2}+2592x=-36x^{2}-3888x+93312+2592x$$

Combine -3888x and 2592x to get -1296x.

$$-36x^{2}+2592x=-36x^{2}-1296x+93312$$

Add 36x^{2} to both sides.

$$-36x^{2}+2592x+36x^{2}=-1296x+93312$$

Combine -36x^{2} and 36x^{2} to get 0.

$$2592x=-1296x+93312$$

Add 1296x to both sides.

$$2592x+1296x=93312$$

Combine 2592x and 1296x to get 3888x.

$$3888x=93312$$

Divide both sides by 3888.

$$x=\frac{93312}{3888}$$

Divide 93312 by 3888 to get 24.

$$x=24$$