Solve 10-15/35-x=15-30/x-45

$$\frac{ 10-15 }{ 35-x } = \frac{ 15-30 }{ x-45 }$$

Solve for x

$$x = \frac{75}{2} = 37\frac{1}{2} = 37.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 35,45 since division by zero is not defined. Multiply both sides of the equation by \left(x-45\right)\left(x-35\right), the least common multiple of 35-x,x-45.

$$\left(45-x\right)\left(10-15\right)=\left(x-35\right)\left(15-30\right)$$

Subtract 15 from 10 to get -5.

$$\left(45-x\right)\left(-5\right)=\left(x-35\right)\left(15-30\right)$$

Use the distributive property to multiply 45-x by -5.

$$-225+5x=\left(x-35\right)\left(15-30\right)$$

Subtract 30 from 15 to get -15.

$$-225+5x=\left(x-35\right)\left(-15\right)$$

Use the distributive property to multiply x-35 by -15.

$$-225+5x=-15x+525$$

Add 15x to both sides.

$$-225+5x+15x=525$$

Combine 5x and 15x to get 20x.

$$-225+20x=525$$

Add 225 to both sides.

$$20x=525+225$$

Add 525 and 225 to get 750.

$$20x=750$$

Divide both sides by 20.

$$x=\frac{750}{20}$$

Reduce the fraction \frac{750}{20} to lowest terms by extracting and canceling out 10.

$$x=\frac{75}{2}$$