Solve 30-40/40-x=40-45/x-45

$$\frac{ 30-40 }{ 40-x } = \frac{ 40-45 }{ x-45 }$$

Solve for x

$$x = \frac{130}{3} = 43\frac{1}{3} \approx 43.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 40,45 since division by zero is not defined. Multiply both sides of the equation by \left(x-45\right)\left(x-40\right), the least common multiple of 40-x,x-45.

$$\left(45-x\right)\left(30-40\right)=\left(x-40\right)\left(40-45\right)$$

Subtract 40 from 30 to get -10.

$$\left(45-x\right)\left(-10\right)=\left(x-40\right)\left(40-45\right)$$

Use the distributive property to multiply 45-x by -10.

$$-450+10x=\left(x-40\right)\left(40-45\right)$$

Subtract 45 from 40 to get -5.

$$-450+10x=\left(x-40\right)\left(-5\right)$$

Use the distributive property to multiply x-40 by -5.

$$-450+10x=-5x+200$$

Add 5x to both sides.

$$-450+10x+5x=200$$

Combine 10x and 5x to get 15x.

$$-450+15x=200$$

Add 450 to both sides.

$$15x=200+450$$

Add 200 and 450 to get 650.

$$15x=650$$

Divide both sides by 15.

$$x=\frac{650}{15}$$

Reduce the fraction \frac{650}{15} to lowest terms by extracting and canceling out 5.

$$x=\frac{130}{3}$$