Solve -3/x-4=4/x-5

$$\frac { - 3 } { x - 4 } = \frac { 4 } { x - 5 }$$

Solve for x

$$x = \frac{31}{7} = 4\frac{3}{7} \approx 4.428571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 4,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-4\right), the least common multiple of x-4,x-5.

$$\left(x-5\right)\left(-3\right)=\left(x-4\right)\times 4$$

Use the distributive property to multiply x-5 by -3.

$$-3x+15=\left(x-4\right)\times 4$$

Use the distributive property to multiply x-4 by 4.

$$-3x+15=4x-16$$

Subtract 4x from both sides.

$$-3x+15-4x=-16$$

Combine -3x and -4x to get -7x.

$$-7x+15=-16$$

Subtract 15 from both sides.

$$-7x=-16-15$$

Subtract 15 from -16 to get -31.

$$-7x=-31$$

Divide both sides by -7.

$$x=\frac{-31}{-7}$$

Fraction \frac{-31}{-7} can be simplified to \frac{31}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{31}{7}$$